share/contrib/diffequations/tests/rtestode_kamke_2_3.mac

   1 (load("contrib_ode"),0);
   2 0$
   3
   4 /* ODE tests - Second order linear equations 201-300
   5
   6   Reference:
   7     E Kamke, Differentialgleichungen Losungsmethoden und Losungen,
   8     Vol 1, Geest & Portig, Leipzig, 1961
   9 */
  10
  11 /* Print ode number*/
  12 (pn_(n_):=print("Kamke ODE 2.",n_),true);
  13 true;
  14
  15 /* Kamke 2. 201  */
  16 (pn_(201),ans:contrib_ode(eqn:x^2*'diff(y,x,2)+x*(2*x+1)*'diff(y,x,1)-4*y,y,x));
  17 [y = kummer_u(-2,-3,-2*x)*%k2/x^2+kummer_m(-2,-3,-2*x)*%k1/x^2];
  18 [method,ode_check(eqn,ans[1])];
  19 [odelin,0];
  20
  21 /* Kamke 2. 202  */
  22 (pn_(202),ans:contrib_ode(eqn:x^2*'diff(y,x,2)-2*x*(x+1)*'diff(y,x,1)+2*(x+1)*y,y,x));
  23 [y = %k2*x*%e^(2*x)+%k1*x];
  24 [method,ode_check(eqn,ans[1])];
  25 [odelin,0];
  26
  27 /* Kamke 2. 203  */
  28 (pn_(203),ans:contrib_ode(eqn:x^2*'diff(y,x,2)+a*x^2*'diff(y,x,1)-2*y,y,x),0);
  29 0$
  30 /*
  31 [y = bessel_y(-3/2,-%i*a*x/2)*%k2*sqrt(-x)*%e^-(a*x/2)
  32     +bessel_j(-3/2,-%i*a*x/2)*%k1*sqrt(-x)*%e^-(a*x/2)];
  33  */
  34 [method,ode_check(eqn,ans[1])];
  35 [odelin,0];
  36
  37 /* Kamke 2. 204  */
  38 (pn_(204),ans:contrib_ode(eqn:x^2*'diff(y,x,2)+(2*b+a)*x^2*'diff(y,x,1)+(b*(b+a)*x^2-2)*y,y,x),0);
  39 0$
  40 /*
  41 [y = bessel_y(-(3/2),-(%i*a*x/2))*%k2*sqrt(-x)*%e^-(b*x+a*x/2)
  42     +bessel_j(-(3/2),-(%i*a*x/2))*%k1*sqrt(-x)*%e^-(b*x+a*x/2)];
  43  */
  44 [method,ode_check(eqn,ans[1])];
  45 [odelin,0];
  46
  47 /* Kamke 2. 205  */
  48 (pn_(205),ans:contrib_ode(eqn:x^2*'diff(y,x,2)+a*x^2*'diff(y,x,1)+f(x)*y,y,x));
  49 false;
  50
  51 /* Kamke 2. 206  */
  52 (pn_(206),ans:contrib_ode(eqn:x^2*'diff(y,x,2)+x*(2*a*x+b)*'diff(y,x,1)+(c*x^2+a*b*x+d)*y,y,x));
  53 [y=%k2*bessel_y(sqrt(-4*d+b^2-2*b+1)/2,-sqrt(c-a^2)*x)*%e^-(a*x)/x^(b/2-1/2)
  54   +%k1*bessel_j(sqrt(-4*d+b^2-2*b+1)/2,-sqrt(c-a^2)*x)*%e^-(a*x)/x^(b/2-1/2)];
  55 [method,ode_check(eqn,ans[1])];
  56 [odelin,0];
  57
  58 /* Kamke 2. 207  */
  59 (pn_(207),ans:contrib_ode(eqn:x^2*'diff(y,x,2)+x*(a*x+b)*'diff(y,x,1)+(a1*x^2+b1*x+c_1)*y,y,x),0);
  60 0$
  61 /*
  62 [y = %k2*kummer_u(4*a1*sqrt(-4*c_1+b^2-2*b+1)/(8*a1-2*a^2)
  63                           -(a^2*sqrt(-4*c_1+b^2-2*b+1)/(8*a1-2*a^2))
  64                           -(2*sqrt(a^2-4*a1)*b1/(8*a1-2*a^2))
  65                           +a*sqrt(a^2-4*a1)*b/(8*a1-2*a^2)+4*a1/(8*a1-2*a^2)
  66                           -(a^2/(8*a1-2*a^2)),sqrt(-4*c_1+b^2-2*b+1)+1,
  67                          -sqrt(a^2-4*a1)*x)
  68                *x^(sqrt(-4*c_1+b^2-2*b+1)/2-(b/2)+1/2)
  69                *%e^(sqrt(a^2-4*a1)*x/2-(a*x/2))
  70           +%k1*kummer_m(4*a1*sqrt(-4*c_1+b^2-2*b+1)/(8*a1-2*a^2)
  71                          -(a^2*sqrt(-4*c_1+b^2-2*b+1)/(8*a1-2*a^2))
  72                          -(2*sqrt(a^2-4*a1)*b1/(8*a1-2*a^2))
  73                          +a*sqrt(a^2-4*a1)*b/(8*a1-2*a^2)+4*a1/(8*a1-2*a^2)
  74                          -(a^2/(8*a1-2*a^2)),sqrt(-4*c_1+b^2-2*b+1)+1,
  75                         -sqrt(a^2-4*a1)*x)
  76               *x^(sqrt(-4*c_1+b^2-2*b+1)/2-(b/2)+1/2)
  77               *%e^(sqrt(a^2-4*a1)*x/2-(a*x/2))];
  78  */
  79 [method,ode_check(eqn,ans[1])];
  80 [odelin,0];
  81
  82 /* Kamke 2. 208  */
  83 (pn_(208),ans:contrib_ode(eqn:x^2*'diff(y,x,2)+x^3*'diff(y,x,1)+(x^2-2)*y,y,x),0);
  84 0$
  85 /*
  86 [y=%k2*(sqrt(2)*sqrt(%pi)*erf(x/sqrt(2))/x-2*%e^-(x^2/2))+%k1/x];
  87  */
  88 [method,ode_check(eqn,ans[1])];
  89 [odelin,0];
  90
  91 /* Kamke 2. 209  */
  92 (pn_(209),ans:contrib_ode(eqn:x^2*'diff(y,x,2)+x*(x^2+2)*'diff(y,x,1)+(x^2-2)*y,y,x),0);
  93 0$
  94 /*
  95 [y = %k2*(sqrt(2)*sqrt(%pi)*%i*%e^-(x^2/2)*erf(%i*x/sqrt(2))/x^2+2/x)
  96           +%k1*%e^-(x^2/2)/x^2];
  97  */
  98 [method,ode_check(eqn,ans[1])];
  99 [odelin,0];
 100
 101 /* Kamke 2. 210  */
 102 (pn_(210),ans:contrib_ode(eqn:x^2*'diff(y,x,2)-2*x*(x^2-a)*'diff(y,x,1)+(2*n*x^2+a*((-1)^n-1))*y,y,x),0);
 103 0$
 104 /*
 105 [y = %k2*kummer_u(sqrt(-4*a*(-1)^n+4*a^2+1)/4-(n/2)-(a/2)+1/4,
 106                        sqrt(-4*a*(-1)^n+4*a^2+1)/2+1,x^2)
 107              *x^(sqrt(-4*a*(-1)^n+4*a^2+1)/2-a+1/2)
 108     +%k1*kummer_m(sqrt(-4*a*(-1)^n+4*a^2+1)/4-(n/2)-(a/2)+1/4,
 109                        sqrt(-4*a*(-1)^n+4*a^2+1)/2+1,x^2)
 110              *x^(sqrt(-4*a*(-1)^n+4*a^2+1)/2-a+1/2)];
 111  */
 112 [method,ode_check(eqn,ans[1])];
 113 [odelin,0];
 114
 115 /* Kamke 2. 211  */
 116 (pn_(211),ans:contrib_ode(eqn:x^2*'diff(y,x,2)+4*x^3*'diff(y,x,1)+(4*x^4+2*x^2+1)*y,y,x));
 117 [y = %k2*x^(sqrt(3)*%i/2+1/2)*%e^-x^2+%k1*x^(1/2-(sqrt(3)*%i/2))*%e^-x^2];
 118 [method,ode_check(eqn,ans[1])];
 119 [odelin,0];
 120
 121 /* Kamke 2. 212  */
 122 (pn_(212),ans:contrib_ode(eqn:x^2*'diff(y,x,2)+x*(a*x^2+b)*'diff(y,x,1)+f(x)*y,y,x));
 123 false;
 124
 125 /* Kamke 2. 213  */
 126 (pn_(213),ans:contrib_ode(eqn:x^2*'diff(y,x,2)+x*(x^3+1)*'diff(y,x,1)-y,y,x),0);
 127 0$
 128 /*
 129  [y = kummer_u(2/3,1/3,x^3/3)*%k2*%e^-(x^3/3)/x
 130      +kummer_m(2/3,1/3,x^3/3)*%k1*%e^-(x^3/3)/x];
 131  */
 132 [method,ode_check(eqn,ans[1])];
 133 [odelin,0];
 134
 135 /* Kamke 2. 214  */
 136 (pn_(214),ans:contrib_ode(eqn:x^2*'diff(y,x,2)+(-x^4+(2*n+2*a+1)*x^2+a*(-1)^n-a^2)*y,y,x),0);
 137 0$
 138 /*
 139 [y = %k2*kummer_u(sqrt(-4*a*(-1)^n+4*a^2+1)/4-(n/2)-(a/2)+1/4,
 140                         sqrt(-4*a*(-1)^n+4*a^2+1)/2+1,x^2)
 141               *x^(sqrt(-4*a*(-1)^n+4*a^2+1)/2+1/2)*%e^-(x^2/2)
 142     +%k1*kummer_m(sqrt(-4*a*(-1)^n+4*a^2+1)/4-(n/2)-(a/2)+1/4,
 143                        sqrt(-4*a*(-1)^n+4*a^2+1)/2+1,x^2)
 144              *x^(sqrt(-4*a*(-1)^n+4*a^2+1)/2+1/2)*%e^-(x^2/2)];
 145  */
 146 [method,ode_check(eqn,ans[1])];
 147 [odelin,0];
 148
 149 /* Kamke 2. 215  */
 150 (pn_(215),ans:contrib_ode(eqn:x^2*'diff(y,x,2)+x*(a*x^n+b)*'diff(y,x,1)+(a1*x^(2*n)+b1*x^n+c_1)*y,y,x));
 151 false;
 152
 153 /* Kamke 2. 216  */
 154 (pn_(216),ans:contrib_ode(eqn:y*(DD+x^b1*C+x^a1*B+x^(2*a1)*A)+x^2*'diff(y,x,2)+x*(a*x^a1+b)*'diff(y,x,1),y,x));
 155 false;
 156
 157 /* Kamke 2. 217  */
 158 (pn_(217),ans:contrib_ode(eqn:x^2*'diff(y,x,2)-(2*x^2*tan(x)-x)*'diff(y,x,1)+(-x*tan(x)-a)*y,y,x));
 159 false;
 160
 161 /* Kamke 2. 218  */
 162 (pn_(218),ans:contrib_ode(eqn:x^2*'diff(y,x,2)+(2*x^2*cot(x)+x)*'diff(y,x,1)+(x*cot(x)+a)*y,y,x));
 163 false;
 164
 165 /* Kamke 2. 219  */
 166 (pn_(219),ans:contrib_ode(eqn:x^2*'diff(y,x,2)+2*x*f(x)*'diff(y,x,1)+(x*'diff(f(x),x,1)+f(x)^2-f(x)+a*x^2+b*x+c)*y,y,x));
 167 false;
 168
 169 /* Kamke 2. 220  */
 170 (pn_(220),ans:contrib_ode(eqn:x^2*'diff(y,x,2)+2*x^2*f(x)*'diff(y,x,1)+(x^2*('diff(f(x),x,1)+f(x)^2+a)-(v-1)*v)*y,y,x));
 171 false;
 172
 173 /* Kamke 2. 221  */
 174 (pn_(221),ans:contrib_ode(eqn:x^2*'diff(y,x,2)+(x-2*x^2*f(x))*'diff(y,x,1)+(x^2*(-'diff(f(x),x,1)+f(x)^2+1)-x*f(x)-v^2)*y,y,x));
 175 false;
 176
 177 /* Kamke 2. 222  */
 178 (pn_(222),ans:contrib_ode(eqn:(x^2+1)*'diff(y,x,2)+x*'diff(y,x,1)+2*y,y,x));
 179 [y=%k1*sin(sqrt(2)*asinh(x))+%k2*cos(sqrt(2)*asinh(x))];
 180 ode_check(eqn,ans[1]);
 181 0;
 182 method;
 183 xformtoconstcoeff;
 184
 185 /* Kamke 2. 223  */
 186 assume(sqrt(x^2+1)+x>0);
 187 [sqrt(x^2+1)+x>0];
 188 (pn_(223),ans:contrib_ode(eqn:(x^2+1)*'diff(y,x,2)+x*'diff(y,x,1)-9*y,y,x));
 189 [y=%i*%k1*sinh(3*asinh(x))+%k2*cosh(3*asinh(x))];
 190 ode_check(eqn,ans[1]);
 191 0;
 192 method;
 193 xformtoconstcoeff;
 194 forget(sqrt(x^2+1)+x>0);
 195 [sqrt(x^2+1)+x>0];
 196
 197 /* Kamke 2. 224  */
 198 (pn_(224),ans:contrib_ode(eqn:(x^2+1)*'diff(y,x,2)+x*'diff(y,x,1)+a*y,y,x));
 199 [y=%k1*sin(sqrt(a)*asinh(x))+%k2*cos(sqrt(a)*asinh(x))];
 200 ode_check(eqn,ans[1]);
 201 0;
 202 method;
 203 xformtoconstcoeff;
 204
 205 /* Kamke 2. 225  */
 206 (pn_(225),ans:contrib_ode(eqn:(x^2+1)*'diff(y,x,2)-x*'diff(y,x,1)+y,y,x),0);
 207 0$
 208 /*
 209 [y = gauss_b(2,2,5/2,1/2-(%i*x/2))*%k2*(-%i*x-1)^(1/4)*(1-%i*x)^(1/4)
 210                                       *(x^2+1)^(5/4)
 211     +gauss_a(2,2,5/2,1/2-(%i*x/2))*%k1*(-%i*x-1)^(1/4)*(1-%i*x)^(1/4)
 212                                      *(x^2+1)^(5/4)];
 213  */
 214 [method,ode_check(eqn,ans[1])];
 215 [odelin,0];
 216
 217 /* Kamke 2. 226  */
 218 (pn_(226),ans:contrib_ode(eqn:(x^2+1)*'diff(y,x,2)+2*x*'diff(y,x,1)-(v-1)*v*y,y,x),0);
 219 0$
 220 /*
 221 [y = %k2*gauss_b(1-v,v,1,1/2-(%i*x/2))*sqrt(-%i*x-1)*sqrt(1-%i*x)
 222          /sqrt(x^2+1)
 223     +%k1*gauss_a(1-v,v,1,1/2-(%i*x/2))*sqrt(-%i*x-1)*sqrt(1-%i*x)
 224          /sqrt(x^2+1)];
 225  */
 226 [method,ode_check(eqn,ans[1])];
 227 [odelin,0];
 228
 229 /* Kamke 2. 227  */
 230 (pn_(227),ans:contrib_ode(eqn:(x^2+1)*'diff(y,x,2)-2*x*'diff(y,x,1)+2*y,y,x),0);
 231 0$
 232 /*
 233 [y = %k2*(x^2*%e^(2*%i*atan(x))+%e^(2*%i*atan(x)))
 234     +%k1*(x^2*%e^-(2*%i*atan(x))+%e^-(2*%i*atan(x)))];
 235  */
 236 [method,ode_check(eqn,ans[1])];
 237 [odelin,0];
 238
 239 /* Kamke 2. 228  */
 240 (pn_(228),ans:contrib_ode(eqn:(x^2+1)*'diff(y,x,2)+3*x*'diff(y,x,1)+a*y,y,x),0);
 241 0$
 242 /*
 243 [y = %k2*gauss_b(sqrt(1-a),-sqrt(1-a),1/2,1/2-(%i*x/2))*(-%i*x-1)^(1/4)
 244              *(1-%i*x)^(1/4)/(x^2+1)^(3/4)
 245      +%k1*gauss_a(sqrt(1-a),-sqrt(1-a),1/2,1/2-(%i*x/2))*(-%i*x-1)^(1/4)
 246              *(1-%i*x)^(1/4)/(x^2+1)^(3/4)];
 247  */
 248 [method,ode_check(eqn,ans[1])];
 249 [odelin,0];
 250
 251 /* Kamke 2. 229  */
 252 (pn_(229),ans:contrib_ode(eqn:(x^2+1)*'diff(y,x,2)+4*x*'diff(y,x,1)+2*y-2*cos(x)+2*x,y,x));
 253 [y=-((6*cos(x)+x^3)/(3*x^2+3))+%k1*x/(x^2+1)+%k2/(x^2+1)];
 254 ode_check(eqn,ans[1]);
 255 0;
 256 method;
 257 variationofparameters;
 258
 259 /* Kamke 2. 230  */
 260 (pn_(230),ans:contrib_ode(eqn:(x^2+1)*'diff(y,x,2)+a*x*'diff(y,x,1)+(a-2)*y,y,x));
 261 [y=%k1*%e^-((a-2)*log(x^2+1)/2)*'integrate(%e^((a-2)*log(x^2+1)/2)/(x^2+1),x)+%k2*%e^-((a-2)*log(x^2+1)/2)];
 262 ode_check(eqn,ans[1]);
 263 0;
 264 method;
 265 exact;
 266
 267 /* Kamke 2. 231  */
 268 (pn_(231),ans:contrib_ode(eqn:(x^2-1)*'diff(y,x,2)-v*(v+1)*y,y,x),0);
 269 0$
 270 /*
 271 [y = %k2*gauss_b(-v-1,v,0,1/2-(x/2))+%k1*gauss_a(-v-1,v,0,1/2-(x/2))];
 272  */
 273 [method,ode_check(eqn,ans[1])];
 274 [odelin,0];
 275
 276 /* Kamke 2. 232 */
 277 (pn_(232),ans:contrib_ode(eqn:(x^2-1)*'diff(y,x,2)-n*(n+1)*y+diff(legendre_p(n,x),x),y,x));
 278 false;
 279
 280 /* Kamke 2. 233 */
 281 (pn_(233),ans:contrib_ode(eqn:(x^2-1)*'diff(y,x,2)-n*(n+1)*y+diff(legendre_q(n,x),x),y,x));
 282 false;
 283
 284 /* Kamke 2. 234  */
 285 (pn_(234),ans:contrib_ode(eqn:(x^2-1)*'diff(y,x,2)+x*'diff(y,x,1)+2,y,x));
 286 [y = -2*log(2*sqrt(x^2-1)+2*x)^2+2*log(2*sqrt(x^2-1)+2*x)^2/2
 287      +%k1*log(2*sqrt(x^2-1)+2*x)+%k2];
 288 ode_check(eqn,ans[1]);
 289 0;
 290 method;
 291 freeofy;
 292
 293 /* Kamke 2. 235  */
 294 (pn_(235),ans:contrib_ode(eqn:(x^2-1)*'diff(y,x,2)+x*'diff(y,x,1)+a*y,y,x));
 295 [y=%k1*sin(sqrt(a)*log(2*sqrt(x^2-1)+2*x))+%k2*cos(sqrt(a)*log(2*sqrt(x^2-1)+2*x))];
 296 ode_check(eqn,ans[1]);
 297 0;
 298 method;
 299 xformtoconstcoeff;
 300
 301 /* Kamke 2. 236  */
 302 (pn_(236),ans:contrib_ode(eqn:(x^2-1)*'diff(y,x,2)+x*'diff(y,x,1)+f(x)*y,y,x));
 303 false;
 304
 305 /* Kamke 2. 237  */
 306 (pn_(237),ans:contrib_ode(eqn:(x^2-1)*'diff(y,x,2)+2*x*'diff(y,x,1),y,x));
 307 [y=%k1*(log(x-1)/2-log(x+1)/2)+%k2];
 308 ode_check(eqn,ans[1]);
 309 0;
 310 method;
 311 exact;
 312
 313 /* Kamke 2. 238  */
 314 (pn_(238),ans:contrib_ode(eqn:(x^2-1)*'diff(y,x,2)+2*x*'diff(y,x,1)-a,y,x));
 315 [y=(a*log(x+1)+a*log(x-1)-2*a)/2+%k1*(log(x-1)/2-log(x+1)/2)+%k2];
 316 ode_check(eqn,ans[1]);
 317 0;
 318 method;
 319 variationofparameters;
 320
 321 /* Kamke 2. 239  */
 322 (pn_(239),ans:contrib_ode(eqn:(x^2-1)*'diff(y,x,2)+2*x*'diff(y,x,1)-L*y,y,x),0);
 323 0$
 324 /*
 325  [y = %k2*gauss_b(sqrt(4*L+1)/2+1/2,1/2-(sqrt(4*L+1)/2),1,1/2-(x/2))
 326      +%k1*gauss_a(sqrt(4*L+1)/2+1/2,1/2-(sqrt(4*L+1)/2),1,1/2-(x/2))];
 327  */
 328 [method,ode_check(eqn,ans[1])];
 329 [odelin,0];
 330
 331 /* Kamke 2. 240  */
 332 (pn_(240),ans:contrib_ode(eqn:(x^2-1)*'diff(y,x,2)+2*x*'diff(y,x,1)-v*(v+1)*y,y,x),0);
 333 0$
 334 /*
 335 [y = %k2*gauss_b(-v,v+1,1,1/2-(x/2))+%k1*gauss_a(-v,v+1,1,1/2-(x/2))];
 336  */
 337 [method,ode_check(eqn,ans[1])];
 338 [odelin,0];
 339
 340 /* Kamke 2. 241  */
 341 (pn_(241),ans:contrib_ode(eqn:(x^2-1)*'diff(y,x,2)-2*x*'diff(y,x,1)+(-v-2)*(v-1)*y,y,x),0);
 342 0$
 343 /*
 344 [y = %k2*gauss_b(-v,v+1,3,1/2-(x/2))*(x-1)^2
 345     +%k1*gauss_a(-v,v+1,3,1/2-(x/2))*(x-1)^2];
 346  */
 347 [method,ode_check(eqn,ans[1])];
 348 [odelin,0];
 349
 350 /* Kamke 2. 242  */
 351 (pn_(242),ans:contrib_ode(eqn:(x^2-1)*'diff(y,x,2)-(3*x+1)*'diff(y,x,1)+(x-x^2)*y,y,x));
 352 [y = %k2*(x^3*('integrate(8*x*%e^(2*x)/(x^4+4*x^3+6*x^2+4*x+1)
 353                                   -(7*%e^(2*x)/(x^4+4*x^3+6*x^2+4*x+1)),x))
 354                 /(x*%e^x+%e^x)
 355                 +3*x^2
 356                   *('integrate(8*x*%e^(2*x)/(x^4+4*x^3+6*x^2+4*x+1)
 357                                 -(7*%e^(2*x)/(x^4+4*x^3+6*x^2+4*x+1)),x))
 358                  /(x*%e^x+%e^x)
 359                 +3*x
 360                   *('integrate(8*x*%e^(2*x)/(x^4+4*x^3+6*x^2+4*x+1)
 361                                 -(7*%e^(2*x)/(x^4+4*x^3+6*x^2+4*x+1)),x))
 362                  /(x*%e^x+%e^x)
 363                 +('integrate(8*x*%e^(2*x)/(x^4+4*x^3+6*x^2+4*x+1)
 364                               -(7*%e^(2*x)/(x^4+4*x^3+6*x^2+4*x+1)),x))
 365                  /(x*%e^x+%e^x)-2*x^2*%e^(2*x)/(x*%e^x+%e^x)
 366                 +3*x*%e^(2*x)/(x*%e^x+%e^x))
 367           +%k1*(x+1)^2*%e^-x];
 368 [method,ode_check(eqn,ans[1])];
 369 [odelin,0];
 370
 371 /* Kamke 2. 243  */
 372 (pn_(243),ans:contrib_ode(eqn:(x^2-1)*'diff(y,x,2)+4*x*'diff(y,x,1)+(x^2+1)*y,y,x),0);
 373 0$
 374 /*
 375 [y = %k2/(x^2*%e^(%i*x)-%e^(%i*x))+%k1*%e^(%i*x)/(x^2-1)];
 376  */
 377 [method,ode_check(eqn,ans[1])];
 378 [odelin,0];
 379
 380 /* Kamke 2. 244  */
 381 (pn_(244),ans:contrib_ode(eqn:(x^2-1)*'diff(y,x,2)+2*(n+1)*x*'diff(y,x,1)+(-v-n-1)*(v-n)*y,y,x),0);
 382 0$
 383 /*
 384  [y = %k2*gauss_b(-v,v+1,n+1,1/2-(x/2))/(x+1)^n
 385      +%k1*gauss_a(-v,v+1,n+1,1/2-(x/2))/(x+1)^n];
 386  */
 387 [method,ode_check(eqn,ans[1])];
 388 [odelin,0];
 389
 390 /* Kamke 2. 245  */
 391 (pn_(245),ans:contrib_ode(eqn:(x^2-1)*'diff(y,x,2)-2*(n-1)*x*'diff(y,x,1)+(-v+n-1)*(v+n)*y,y,x),0);
 392 0$
 393 /*
 394 [y = %k2*gauss_b(-v,v+1,n+1,1/2-(x/2))*(x-1)^n
 395     +%k1*gauss_a(-v,v+1,n+1,1/2-(x/2))*(x-1)^n];
 396  */
 397 [method,ode_check(eqn,ans[1])];
 398 [odelin,0];
 399
 400 /* Kamke 2. 246  */
 401 (pn_(246),ans:contrib_ode(eqn:(x^2-1)*'diff(y,x,2)-2*(v-1)*x*'diff(y,x,1)-2*v*y,y,x));
 402 [y=%k1*%e^(v*log(x^2-1))*'integrate(%e^-(v*log(x^2-1))/(x^2-1),x)+%k2*%e^(v*log(x^2-1))];
 403 ode_check(eqn,ans[1]);
 404 0;
 405 method;
 406 exact;
 407
 408 /* Kamke 2. 247  */
 409 (pn_(247),ans:contrib_ode(eqn:(x^2-1)*'diff(y,x,2)+2*a*x*'diff(y,x,1)+(a-1)*a*y,y,x),0);
 410 0$
 411 /*
 412  [y = %k2*(x+1)^(1-a)*'integrate((x+1)^a/((x-1)^a*x^2+2*(x-1)^a*x+(x-1)^a),x)
 413      +%k1*(x+1)^(1-a)];
 414  */
 415 [method,ode_check(eqn,ans[1])];
 416 [odelin,0];
 417
 418 /* Kamke 2. 248  */
 419 /* Take a long time
 420 (pn_(248),ans:contrib_ode(eqn:(x^2-1)*'diff(y,x,2)+a*x*'diff(y,x,1)+(b*x^2+c*x+d)*y,y,x));
 421 false;
 422 */
 423
 424 /* Kamke 2. 249  */
 425 /* Take a long time
 426 (pn_(249),ans:contrib_ode(eqn:(x^2-1)*'diff(y,x,2)+(a*x+b)*'diff(y,x,1)+c*y,y,x));
 427 false;
 428 */
 429
 430 /* Kamke 2. 250  */
 431 (pn_(250),ans:contrib_ode(eqn:(x^2-a^2)*'diff(y,x,2)+8*x*'diff(y,x,1)+12*y,y,x),0);
 432 0$
 433 /*
 434 [y=%k2*(3*x^2/(x^6-3*a^2*x^4+3*a^4*x^2-a^6)+a^2/(x^6-3*a^2*x^4+3*a^4*x^2-a^6))
 435           +%k1/(x^3+3*a*x^2+3*a^2*x+a^3)];
 436  */
 437 [method,ode_check(eqn,ans[1])];
 438 [odelin,0];
 439
 440 /* Kamke 2. 251  */
 441 (pn_(251),ans:contrib_ode(eqn:x*(x+1)*'diff(y,x,2)-(x-1)*'diff(y,x,1)+y,y,x));
 442 [y = gauss_b(2,2,1,-x)*%k2*(x+1)^3+gauss_a(2,2,1,-x)*%k1*(x+1)^3];
 443 [method,ode_check(eqn,ans[1])];
 444 [odelin,0];
 445
 446 /* Kamke 2. 252  */
 447 (pn_(252),ans:contrib_ode(eqn:x*(x+1)*'diff(y,x,2)+(a*x+b)*'diff(y,x,1)+c*y,y,x),0);
 448 0$
 449 /*
 450 [y = %k2*gauss_b(sqrt(-4*c+a^2-2*a+1)/2+a/2-(1/2),
 451                        -(sqrt(-4*c+a^2-2*a+1)/2)+a/2-(1/2),b,-x)
 452     +%k1*gauss_a(sqrt(-4*c+a^2-2*a+1)/2+a/2-(1/2),
 453                        -(sqrt(-4*c+a^2-2*a+1)/2)+a/2-(1/2),b,-x)];
 454  */
 455 [method,ode_check(eqn,ans[1])];
 456 [odelin,0];
 457
 458 /* Kamke 2. 253  */
 459 (pn_(253),ans:contrib_ode(eqn:x*(x+1)*'diff(y,x,2)+(3*x+2)*'diff(y,x,1)+y,y,x));
 460 [y=%k1*log(x+1)/x+%k2/x];
 461 ode_check(eqn,ans[1]);
 462 0;
 463 method;
 464 exact;
 465
 466 /* Kamke 2. 254  */
 467 (pn_(254),ans:contrib_ode(eqn:(x^2+x-2)*'diff(y,x,2)+(x^2-x)*'diff(y,x,1)+(-6*x^2-7*x)*y,y,x),0);
 468 0$
 469 /*
 470 [y = %k2*(2*x^2*%e^(2*x)
 471                   *('integrate(3*x/(x^3*%e^(5*x)-3*x^2*%e^(5*x)+3*x*%e^(5*x)
 472                                                 -%e^(5*x))
 473                                 +2/(x^3*%e^(5*x)-3*x^2*%e^(5*x)+3*x*%e^(5*x)
 474                                                 -%e^(5*x)),x))
 475                 /(x-1)
 476                 -4*x*%e^(2*x)
 477                   *('integrate(3*x/(x^3*%e^(5*x)-3*x^2*%e^(5*x)+3*x*%e^(5*x)
 478                                                 -%e^(5*x))
 479                                 +2/(x^3*%e^(5*x)-3*x^2*%e^(5*x)+3*x*%e^(5*x)
 480                                                 -%e^(5*x)),x))
 481                  /(x-1)
 482                 +2*%e^(2*x)
 483                   *('integrate(3*x/(x^3*%e^(5*x)-3*x^2*%e^(5*x)+3*x*%e^(5*x)
 484                                                 -%e^(5*x))
 485                                 +2/(x^3*%e^(5*x)-3*x^2*%e^(5*x)+3*x*%e^(5*x)
 486                                                 -%e^(5*x)),x))
 487                  /(x-1)+20*expintegral_e(2,5*x-5)*x*%e^(2*x-5)/(x-1)
 488                 -20*expintegral_e(2,5*x-5)*%e^(2*x-5)/(x-1)
 489                 +x^2/(x*%e^(3*x)-%e^(3*x))+4*x/(x*%e^(3*x)-%e^(3*x)))
 490           +%k1*(x*%e^(2*x)-%e^(2*x))];
 491  */
 492 [method,ode_check(eqn,ans[1])];
 493 [odelin,0];
 494
 495 /* Kamke 2. 255  */
 496 (pn_(255),ans:contrib_ode(eqn:(x-1)*x*'diff(y,x,2)+a*'diff(y,x,1)-2*y,y,x));
 497 [y = %k1*%e^((a+1)*log(x)+(1-a)*log(x-1))
 498               *'integrate(%e^(-(a+1)*log(x)-(1-a)*log(x-1))/(x^2-x),x)
 499     +%k2*%e^((a+1)*log(x)+(1-a)*log(x-1))];
 500 ode_check(eqn,ans[1]);
 501 0;
 502 method;
 503 exact;
 504
 505 /* Kamke 2. 256  */
 506 (pn_(256),ans:contrib_ode(eqn:(x-1)*x*'diff(y,x,2)+(2*x-1)*'diff(y,x,1)-v*(v+1)*y,y,x));
 507 [y = %k2*gauss_b(-v,v+1,1,x)+%k1*gauss_a(-v,v+1,1,x)];
 508 [method,ode_check(eqn,ans[1])];
 509 [odelin,0];
 510
 511 /* Kamke 2. 257  */
 512 (pn_(257),ans:contrib_ode(eqn:(x-1)*x*'diff(y,x,2)+((a+1)*x+b)*'diff(y,x,1),y,x));
 513 [y=%k1*'integrate(%e^(b*log(x)-b*log(x-1)-a*log(x-1))/(x-1),x)+%k2];
 514 ode_check(eqn,ans[1]);
 515 0;
 516 method;
 517 freeofy;
 518
 519 /* Kamke 2. 258  */
 520 (pn_(258),ans:contrib_ode(eqn:(x-1)*x*'diff(y,x,2)+(a*x+b)*'diff(y,x,1)+c*y,y,x),0);
 521 0$
 522 /*
 523  [y = %k2*gauss_b(sqrt(-4*c+a^2-2*a+1)/2+a/2-(1/2),
 524                        -(sqrt(-4*c+a^2-2*a+1)/2)+a/2-(1/2),-b,x)
 525      +%k1*gauss_a(sqrt(-4*c+a^2-2*a+1)/2+a/2-(1/2),
 526                        -(sqrt(-4*c+a^2-2*a+1)/2)+a/2-(1/2),-b,x)];
 527  */
 528 [method,ode_check(eqn,ans[1])];
 529 [odelin,0];
 530
 531 /* Kamke 2. 259  */
 532 (pn_(259),ans:contrib_ode(eqn:(x-1)*x*'diff(y,x,2)+((a+1)*x+b)*'diff(y,x,1)-l*y,y,x),0);
 533 0$
 534 /*
 535 [y = %k2*gauss_b(sqrt(4*l+a^2)/2+a/2,a/2-(sqrt(4*l+a^2)/2),-b,x)
 536     +%k1*gauss_a(sqrt(4*l+a^2)/2+a/2,a/2-(sqrt(4*l+a^2)/2),-b,x)];
 537  */
 538 [method,ode_check(eqn,ans[1])];
 539 [odelin,0];
 540
 541 /* Kamke 2. 260  */
 542 (pn_(260),ans:contrib_ode(eqn:(x-1)*x*'diff(y,x,2)+((b1+a1+1)*x-d1)*'diff(y,x,1)+a1*b1*d1,y,x));
 543 [y=%k2-'integrate(%e^(-d1*log(x)-b1*log(x-1)-a1*log(x-1))*(a1*b1*d1*%e^(d1*log(x-1))*'integrate(%e^(d1*log(x)-d1*log(x-1)+b1*log(x-1)+a1*log(x-1))/x,x)-%k1*%e^(d1*log(x-1)))/(x-1),x)];
 544 ode_check(eqn,ans[1]);
 545 0;
 546 method;
 547 freeofy;
 548
 549 /* Kamke 2. 261  */
 550 (pn_(261),ans:contrib_ode(eqn:x*(x+2)*'diff(y,x,2)+2*(-l*x^2+(n-2*l+1)*x+n+1)*'diff(y,x,1)+(2*l*(p-n-1)*x+2*l*p+m)*y,y,x));
 551 false;
 552
 553 /* Kamke 2. 262  */
 554 (pn_(262),ans:contrib_ode(eqn:(x+1)^2*'diff(y,x,2)+(x^2+x-1)*'diff(y,x,1)+(-x-2)*y,y,x),0);
 555 0$
 556 /*
 557 [y = %k2*%e^-x*'integrate(x*%e^(x^2/(x+1)+x/(x+1)-(1/(x+1)))
 558                            +%e^(x^2/(x+1)+x/(x+1)-(1/(x+1))),x)
 559     +%k1*%e^-x];
 560  */
 561 [method,ode_check(eqn,ans[1])];
 562 [odelin,0];
 563
 564 /* Kamke 2. 263 */
 565 (pn_(263),ans:contrib_ode(eqn:x*(x+3)*'diff(y,x,2)+(3*x-1)*'diff(y,x,1)+y+(-20*x-30)*(x^2+3*x)^(7/3),y,x));
 566 [y=%e^-(7*log(x+3)/3)*(%e^(4*log(x)/3)*'integrate(x^(1/3)*(x+3)^(1/3)*(-20*x^5-150*x^4-360*x^3-270*x^2)*'integrate(%e^(7*log(x+3)/3-4*log(x)/3)/(x^2+3*x),x),x)-%e^(4*log(x)/3)*('integrate(x^(1/3)*(x+3)^(1/3)*(-20*x^5-150*x^4-360*x^3-270*x^2),x))*'integrate(%e^(7*log(x+3)/3-4*log(x)/3)/(x^2+3*x),x))+%k1*%e^(4*log(x)/3-7*log(x+3)/3)*'integrate(%e^(7*log(x+3)/3-4*log(x)/3)/(x^2+3*x),x)+%k2*%e^(4*log(x)/3-7*log(x+3)/3)];
 567 [method,radcan(ode_check(eqn,ans[1]))];
 568 [variationofparameters,0];
 569
 570 /* Kamke 2. 264  */
 571 (pn_(264),ans:contrib_ode(eqn:(x^2+3*x+4)*'diff(y,x,2)+(x^2+x+1)*'diff(y,x,1)+(-2*x-3)*y,y,x));
 572 [y = %k2*%e^-x+%k1*(x^2+x+3)];
 573 [method,ode_check(eqn,ans[1])];
 574 [odelin,0];
 575
 576 /* Kamke 2. 265
 577    2016-10:  Solvable with recent fixes to algsys.  Perhaps fragile solution */
 578 (pn_(265),ans:contrib_ode(eqn:(x-2)*(x-1)*'diff(y,x,2)-(2*x-3)*'diff(y,x,1)+y,y,x));
 579 [y = gauss_b((sqrt(5)+5)/2,-((sqrt(5)-5)/2),3,x-1)*%k2*(x-2)^2*(x-1)^2
 580     +gauss_a((sqrt(5)+5)/2,-((sqrt(5)-5)/2),3,x-1)*%k1*(x-2)^2*(x-1)^2];
 581 [method,ode_check(eqn,ans[1])];
 582 [odelin,0];
 583
 584
 585 /* Kamke 2. 266  */
 586 (pn_(266),ans:contrib_ode(eqn:(x-2)^2*'diff(y,x,2)-(x-2)*'diff(y,x,1)-3*y,y,x));
 587 [y=%k2*(x-2)^3-%k1*(x-2)^3/(4*x^4-32*x^3+96*x^2-128*x+64)];
 588 ode_check(eqn,ans[1]);
 589 0;
 590 method;
 591 exact;
 592
 593 /* Kamke 2. 267  */
 594 (pn_(267),ans:contrib_ode(eqn:2*x^2*'diff(y,x,2)-(2*x^2-5*x+l)*'diff(y,x,1)+(1-4*x)*y,y,x));
 595 [y=%k1*%e^((-log(x)+2*x-l/x)/2)*('integrate(%e^-((-log(x)+2*x-l/x)/2)/x^2,x))/2+%k2*%e^((-log(x)+2*x-l/x)/2)];
 596 ode_check(eqn,ans[1]);
 597 0;
 598 method;
 599 exact;
 600
 601 /* Kamke 2. 268  */
 602 (pn_(268),ans:contrib_ode(eqn:2*(x-1)*x*'diff(y,x,2)+(2*x-1)*'diff(y,x,1)+(a*x+b)*y,y,x));
 603 false;
 604
 605 /* Kamke 2. 269  */
 606 (pn_(269),ans:contrib_ode(eqn:2*(x-1)*x*'diff(y,x,2)+((2*v+5)*x-2*v-3)*'diff(y,x,1)+(v+1)*y,y,x),0);
 607 0$
 608 /*
 609 [y = %k2*gauss_b(-v,1/2,1/2-v,x)*x^(-v-1/2)
 610     +%k1*gauss_a(-v,1/2,1/2-v,x)*x^(-v-1/2)];
 611  */
 612 [method,ode_check(eqn,ans[1])];
 613 [odelin,0];
 614
 615 /* Kamke 2. 270  */
 616 (pn_(270),ans:contrib_ode(eqn:(2*x^2+6*x+4)*'diff(y,x,2)+(10*x^2+21*x+8)*'diff(y,x,1)+(12*x^2+17*x+8)*y,y,x));
 617 [y = %k2*(x+2)^4*%e^-(3*x)*'integrate((x+1)^(3/2)*%e^x/(x^5+10*x^4+40*x^3+80*x^2+80*x+32),x)
 618     +%k1*(x+2)^4*%e^-(3*x)];
 619 [method,ode_check(eqn,ans[1])];
 620 [odelin,0];
 621
 622 /* Kamke 2. 271  */
 623 (pn_(271),ans:contrib_ode(eqn:4*x^2*'diff(y,x,2)+y,y,x));
 624 [y=%e^(log(x)/2)*(%k2*log(x)/2+%k1)];
 625 ode_check(eqn,ans[1]);
 626 0;
 627 method;
 628 xformtoconstcoeff;
 629
 630 /* Kamke 2. 272  */
 631 (pn_(272),ans:contrib_ode(eqn:4*x^2*'diff(y,x,2)+(4*a^2*x^2+1)*y,y,x));
 632 [y = bessel_y(0,-a*x)*%k2*sqrt(-x)+bessel_j(0,-a*x)*%k1*sqrt(-x)];
 633 [method,ode_check(eqn,ans[1])];
 634 [odelin,0];
 635
 636 /* Kamke 2. 273  */
 637 (pn_(273),ans:contrib_ode(eqn:4*x^2*'diff(y,x,2)-(x^2-4*k*x+4*m^2-1)*y,y,x),0);
 638 0$
 639 /*
 640 [y = %k2*kummer_u(-m+k+1/2,1-2*m,-x)*(-x)^(1/2-m)*%e^(x/2)
 641     +%k1*kummer_m(-m+k+1/2,1-2*m,-x)*(-x)^(1/2-m)*%e^(x/2)];
 642  */
 643 [method,ode_check(eqn,ans[1])];
 644 [odelin,0];
 645
 646 /* Kamke 2. 274  */
 647 (pn_(274),ans:contrib_ode(eqn:4*x^2*'diff(y,x,2)+4*x*'diff(y,x,1)+(x-v^2)*y,y,x));
 648 [y = %k2*bessel_y(v,sqrt(x))+%k1*bessel_j(v,sqrt(x))];
 649 [method,ode_check(eqn,ans[1])];
 650 [odelin,0];
 651
 652 /* Kamke 2. 275  */
 653 (pn_(275),ans:contrib_ode(eqn:4*x^2*'diff(y,x,2)+4*x*'diff(y,x,1)+(-x^2+2*(-m+2*l+1)*x-m^2+1)*y,y,x));
 654 [y = (%k2*kummer_u(-((sqrt(m-1)*sqrt(m+1)+m-2*l-2)/2),
 655                           1-sqrt(m-1)*sqrt(m+1),-x)*%e^(x/2))
 656           /x^((sqrt(m-1)*sqrt(m+1))/2)
 657     +(%k1*kummer_m(-((sqrt(m-1)*sqrt(m+1)+m-2*l-2)/2),
 658                            1-sqrt(m-1)*sqrt(m+1),-x)*%e^(x/2))
 659           /x^((sqrt(m-1)*sqrt(m+1))/2)];
 660 [method,ode_check(eqn,ans[1])];
 661 [odelin,0];
 662
 663
 664 /* Kamke 2. 276  */
 665 (pn_(276),ans:contrib_ode(eqn:4*x^2*'diff(y,x,2)+4*x*'diff(y,x,1)+(-4*x^2-1)*y-4*x^(3/2)*%e^x,y,x));
 666 [y=((2*x-1)*%e^x)/(4*sqrt(x))+(%k2*%e^x)/sqrt(x)+(%k1*%e^-x)/sqrt(x)];
 667 [method,ode_check(eqn,ans[1])];
 668 [kovacic,0];
 669
 670 /* Kamke 2. 277  */
 671 (pn_(277),ans:contrib_ode(eqn:4*x^2*'diff(y,x,2)+4*x*'diff(y,x,1)+(-a*x^2-1)*y,y,x));
 672 [y = %k2*%e^(sqrt(a)*x/2)/sqrt(x)+%k1*%e^-(sqrt(a)*x/2)/sqrt(x)];
 673 [method,ode_check(eqn,ans[1])];
 674 [odelin,0];
 675
 676 /* Kamke 2. 278  */
 677 (pn_(278),ans:contrib_ode(eqn:4*x^2*'diff(y,x,2)+4*x*'diff(y,x,1)+f(x)*y,y,x));
 678 false;
 679
 680 /* Kamke 2. 279  */
 681 (pn_(279),ans:contrib_ode(eqn:4*x^2*'diff(y,x,2)+5*x*'diff(y,x,1)-y-log(x),y,x));
 682 [y=-log(x)+%k1*x^(sqrt(17)/8-1/8)+%k2*x^(-sqrt(17)/8-1/8)-1];
 683 ode_check(eqn,ans[1]);
 684 0;
 685 method;
 686 variationofparameters;
 687
 688 /* Kamke 2. 280  */
 689 (pn_(280),ans:contrib_ode(eqn:4*x^2*'diff(y,x,2)+8*x*'diff(y,x,1)+(-4*x^2-12*x-3)*y,y,x));
 690 [y = gamma_incomplete(-2,2*x)*%k2*sqrt(x)*%e^x+%k1*sqrt(x)*%e^x];
 691 [method,ode_check(eqn,ans[1])];
 692 [odelin,0];
 693
 694 /* Kamke 2. 281  */
 695 (pn_(281),ans:contrib_ode(eqn:4*x^2*'diff(y,x,2)-4*x*(2*x-1)*'diff(y,x,1)+(4*x^2-4*x-1)*y,y,x));
 696 [y = %k2*sqrt(x)*%e^x+%k1*%e^x/sqrt(x)];
 697 [method,ode_check(eqn,ans[1])];
 698 [odelin,0];
 699
 700 /* Kamke 2. 282  */
 701 (pn_(282),ans:contrib_ode(eqn:4*x^2*'diff(y,x,2)+4*x^3*'diff(y,x,1)+(x^2-4)*(x^2+6)*y,y,x));
 702 [y = %k2*x^3*%e^-(x^2/4)+%k1*%e^-(x^2/4)/x^2];
 703 [method,ode_check(eqn,ans[1])];
 704 [odelin,0];
 705
 706 /* Kamke 2. 283  */
 707 assume(x>0);
 708 [x>0];
 709 (pn_(283),ans:contrib_ode(eqn:4*x^2*'diff(y,x,2)+4*x^2*log(x)*'diff(y,x,1)+(x^2*log(x)^2+2*x-8)*y-4*x^2*%e^(x/2)/sqrt(x^x),y,x));
 710 [y = (3*x^2*%e^(x/2)*log(x)-x^2*%e^(x/2))/(9*x^(x/2))
 711     +%k2*x^(2-x/2)*%e^(x/2)+%k1*x^((-x/2)-1)*%e^(x/2)];
 712 [method,radcan(ode_check(eqn,ans[1]))];
 713 [kovacic,0];
 714 forget(x>0);
 715 [x>0];
 716
 717 /* Kamke 2. 284  */
 718 (pn_(284),ans:contrib_ode(eqn:(2*x+1)^2*'diff(y,x,2)-2*(2*x+1)*'diff(y,x,1)-12*y-3*x-1,y,x));
 719 [y=-%k1*(2*x+1)^3/(128*x^4+256*x^3+192*x^2+64*x+8)-(72*x^2+56*x+7)/(384*x+192)+%k2*(2*x+1)^3];
 720 ode_check(eqn,ans[1]);
 721 0;
 722 method;
 723 variationofparameters;
 724
 725 /* Kamke 2. 285  */
 726 (pn_(285),ans:contrib_ode(eqn:x*(4*x-1)*'diff(y,x,2)+((4*a+2)*x-a)*'diff(y,x,1)+(a-1)*a*y,y,x),0);
 727 0$
 728 /*
 729 [y = %k2*gauss_b(a/2,a/2+1/2,a,4*x)*sqrt(4*x-1)
 730     +%k1*gauss_a(a/2,a/2+1/2,a,4*x)*sqrt(4*x-1)];
 731  */
 732 [method,ode_check(eqn,ans[1])];
 733 [odelin,0];
 734
 735 /* Kamke 2. 286  */
 736 (pn_(286),ans:contrib_ode(eqn:(3*x-1)^2*'diff(y,x,2)+3*(3*x-1)*'diff(y,x,1)-9*y-log(3*x-1)^2,y,x));
 737 [y=-((log(3*x-1)^2+2)/9)-%k1*(3*x-1)/(54*x^2-36*x+6)+%k2*(3*x-1)];
 738 ode_check(eqn,ans[1]);
 739 0;
 740 method;
 741 variationofparameters;
 742
 743 /* Kamke 2. 287  */
 744 (pn_(287),ans:contrib_ode(eqn:9*(x-1)*x*'diff(y,x,2)+3*(2*x-1)*'diff(y,x,1)-20*y,y,x));
 745 [y = gauss_b(-1,2,5/3,x)*%k2*x^(2/3)+gauss_a(-1,2,5/3,x)*%k1*x^(2/3)];
 746 [method,ode_check(eqn,ans[1])];
 747 [odelin,0];
 748
 749 /* Kamke 2. 288  */
 750 (pn_(288),ans:contrib_ode(eqn:16*x^2*'diff(y,x,2)+(4*x+3)*y,y,x));
 751 [y = bessel_y(-1/2,sqrt(x))*%k2*sqrt(x)
 752     +bessel_j(-1/2,sqrt(x))*%k1*sqrt(x)];
 753 [method,ode_check(eqn,ans[1])];
 754 [odelin,0];
 755
 756 /* Kamke 2. 289  */
 757 (pn_(289),ans:contrib_ode(eqn:16*x^2*'diff(y,x,2)+32*x*'diff(y,x,1)+(-4*x-5)*y,y,x));
 758 [y = bessel_y(-3/2,sqrt(-x))*%k2*sqrt(-x)/x
 759     +bessel_j(-3/2,sqrt(-x))*%k1*sqrt(-x)/x];
 760 [method,ode_check(eqn,ans[1])];
 761 [odelin,0];
 762
 763 /* Kamke 2. 290  */
 764 assume(x>0);
 765 [x>0];
 766 (pn_(290),ans:contrib_ode(eqn:(27*x^2+4)*'diff(y,x,2)+27*x*'diff(y,x,1)-3*y,y,x));
 767 [y=%i*%k1*sinh(asinh(27*x/(2*3^(3/2)))/3)+%k2*cosh(asinh(27*x/(2*3^(3/2)))/3)];
 768 ode_check(eqn,ans[1]);
 769 0;
 770 method;
 771 xformtoconstcoeff;
 772 forget(x>0);
 773 [x>0];
 774
 775 /* Kamke 2. 291  */
 776 (pn_(291),ans:contrib_ode(eqn:48*(x-1)*x*'diff(y,x,2)+(152*x-40)*'diff(y,x,1)+53*y,y,x));
 777 [y = (gauss_b((sqrt(2)*sqrt(5)-3)/12,-((sqrt(2)*sqrt(5)+3)/12),5/6,x)
 778           *%k2)
 779           /(x-1)^(4/3)
 780     +(gauss_a((sqrt(2)*sqrt(5)-3)/12,-((sqrt(2)*sqrt(5)+3)/12),5/6,x)*%k1)
 781            /(x-1)^(4/3)];
 782 [method,ode_check(eqn,ans[1])];
 783 [odelin,0];
 784
 785 /* Kamke 2. 292  */
 786 (pn_(292),ans:contrib_ode(eqn:50*(x-1)*x*'diff(y,x,2)+25*(2*x-1)*'diff(y,x,1)-2*y,y,x));
 787 [y = %i*%k1*sinh(log(5*2^(3/2)*sqrt(50*x^2-50*x)+100*x-50)/5)
 788        +%k2*cosh(log(5*2^(3/2)*sqrt(50*x^2-50*x)+100*x-50)/5)];
 789 [method,ode_check(eqn,ans[1])];
 790 [xformtoconstcoeff,0];
 791
 792 /* Kamke 2. 293  */
 793 (pn_(293),ans:contrib_ode(eqn:144*(x-1)*x*'diff(y,x,2)+(120*x-48)*'diff(y,x,1)+y,y,x));
 794 [y = gauss_b(7/12,7/12,5/3,x)*%k2*x^(2/3)
 795     +gauss_a(7/12,7/12,5/3,x)*%k1*x^(2/3)];
 796 [method,ode_check(eqn,ans[1])];
 797 [odelin,0];
 798
 799 /* Kamke 2. 294  */
 800 (pn_(294),ans:contrib_ode(eqn:144*(x-1)*x*'diff(y,x,2)+(168*x-96)*'diff(y,x,1)+y,y,x));
 801 [y = gauss_b(5/12,5/12,4/3,x)*%k2*x^(1/3)
 802     +gauss_a(5/12,5/12,4/3,x)*%k1*x^(1/3)];
 803 [method,ode_check(eqn,ans[1])];
 804 [odelin,0];
 805
 806 /* Kamke 2. 295  */
 807 (pn_(295),ans:contrib_ode(eqn:a*x^2*'diff(y,x,2)+b*x*'diff(y,x,1)+(c*x^2+d*x+f)*y,y,x));
 808 false;
 809
 810 /* Kamke 2. 296  */
 811 (pn_(296),ans:contrib_ode(eqn:a2*x^2*'diff(y,x,2)+(a1*x^2+b1*x)*'diff(y,x,1)+(a0*x^2+b0*x+c_0)*y,y,x),0);
 812 0$
 813 /*
 814 [y = %k2*kummer_u(4*a0*a2*sqrt(-4*a2*c_0+b1^2-2*a2*b1+a2^2)
 815                          /(8*a0*a2^2-2*a1^2*a2)
 816                          -(a1^2*sqrt(-4*a2*c_0+b1^2-2*a2*b1+a2^2)
 817                           /(8*a0*a2^2-2*a1^2*a2))
 818                          +a1*sqrt(a1^2-4*a0*a2)*b1/(8*a0*a2^2-2*a1^2*a2)
 819                          -(2*a2*sqrt(a1^2-4*a0*a2)*b0/(8*a0*a2^2-2*a1^2*a2))
 820                          +4*a0*a2^2/(8*a0*a2^2-2*a1^2*a2)
 821                          -(a1^2*a2/(8*a0*a2^2-2*a1^2*a2)),
 822                         sqrt(-4*a2*c_0+b1^2-2*a2*b1+a2^2)/a2+1,
 823                         -(sqrt(a1^2-4*a0*a2)*x/a2))
 824               *x^(sqrt(-4*a2*c_0+b1^2-2*a2*b1+a2^2)/(2*a2)-(b1/(2*a2))+1/2)
 825               *%e^(sqrt(a1^2-4*a0*a2)*x/(2*a2)-(a1*x/(2*a2)))
 826          +%k1*kummer_m(4*a0*a2*sqrt(-4*a2*c_0+b1^2-2*a2*b1+a2^2)
 827                         /(8*a0*a2^2-2*a1^2*a2)
 828                         -(a1^2*sqrt(-4*a2*c_0+b1^2-2*a2*b1+a2^2)
 829                          /(8*a0*a2^2-2*a1^2*a2))
 830                         +a1*sqrt(a1^2-4*a0*a2)*b1/(8*a0*a2^2-2*a1^2*a2)
 831                         -(2*a2*sqrt(a1^2-4*a0*a2)*b0/(8*a0*a2^2-2*a1^2*a2))
 832                         +4*a0*a2^2/(8*a0*a2^2-2*a1^2*a2)
 833                         -(a1^2*a2/(8*a0*a2^2-2*a1^2*a2)),
 834                        sqrt(-4*a2*c_0+b1^2-2*a2*b1+a2^2)/a2+1,
 835                        -(sqrt(a1^2-4*a0*a2)*x/a2))
 836              *x^(sqrt(-4*a2*c_0+b1^2-2*a2*b1+a2^2)/(2*a2)-(b1/(2*a2))+1/2)
 837              *%e^(sqrt(a1^2-4*a0*a2)*x/(2*a2)-(a1*x/(2*a2)))];
 838  */
 839 [method,ode_check(eqn,ans[1])];
 840 [odelin,0];
 841
 842 /* Kamke 2. 297  */
 843 assume(a>0);
 844 [a>0];
 845 (pn_(297),ans:contrib_ode(eqn:(a*x^2+1)*'diff(y,x,2)+a*x*'diff(y,x,1)+b*y,y,x));
 846 [y=%k1*sin(sqrt(b)*asinh(sqrt(a)*x)/sqrt(a))+%k2*cos(sqrt(b)*asinh(sqrt(a)*x)/sqrt(a))];
 847 ode_check(eqn,ans[1]);
 848 0;
 849 method;
 850 xformtoconstcoeff;
 851 forget(a>0);
 852 [a>0];
 853
 854 /* Kamke 2. 298  FIXME 2015-04-07 hangs in odelin */
 855 /*
 856 (pn_(298),ans:contrib_ode(eqn:(a*x^2+1)*'diff(y,x,2)+b*x*'diff(y,x,1)+c*y,y,x));
 857 [y = %k2*(sqrt(-a)*gauss_b(sqrt(-4*a*c+b^2-2*a*b+a^2)/(2*a)+1/2,
 858                              1/2-(sqrt(-4*a*c+b^2-2*a*b+a^2)/(2*a)),b/(2*a),
 859                              1/2-(sqrt(-a)*x/2))*x*(1-sqrt(-a)*x)^(b/(4*a))
 860                /((-sqrt(-a)*x-1)^(b/(4*a))*(a*x^2+1)^(b/(4*a)))
 861                   +gauss_b(sqrt(-4*a*c+b^2-2*a*b+a^2)/(2*a)+1/2,
 862                              1/2-(sqrt(-4*a*c+b^2-2*a*b+a^2)/(2*a)),b/(2*a),
 863                              1/2-(sqrt(-a)*x/2))
 864                 *x*(1-sqrt(-a)*x)^(b/(4*a))
 865                 /((-sqrt(-a)*x-1)^(b/(4*a))*(a*x^2+1)^(b/(4*a))))
 866      +%k1*(sqrt(-a)*gauss_a(sqrt(-4*a*c+b^2-2*a*b+a^2)/(2*a)+1/2,
 867                              1/2-(sqrt(-4*a*c+b^2-2*a*b+a^2)/(2*a)),b/(2*a),
 868                              1/2-(sqrt(-a)*x/2))*x*(1-sqrt(-a)*x)^(b/(4*a))
 869                /((-sqrt(-a)*x-1)^(b/(4*a))*(a*x^2+1)^(b/(4*a)))
 870                    +gauss_a(sqrt(-4*a*c+b^2-2*a*b+a^2)/(2*a)+1/2,
 871                              1/2-(sqrt(-4*a*c+b^2-2*a*b+a^2)/(2*a)),b/(2*a),
 872                              1/2-(sqrt(-a)*x/2))
 873                *(1-sqrt(-a)*x)^(b/(4*a))
 874                /((-sqrt(-a)*x-1)^(b/(4*a))*(a*x^2+1)^(b/(4*a))))];
 875 [y = %k2*(sqrt(-a)*gauss_b(sqrt(-4*a*c+b^2-2*a*b+a^2)/(2*a)+1/2,
 876                                  1/2-(sqrt(-4*a*c+b^2-2*a*b+a^2)/(2*a)),b/(2*a),
 877                                  1/2-(sqrt(-a)*x/2))*x*(1-sqrt(-a)*x)^(b/(4*a))
 878                /((-sqrt(-a)*x-1)^(b/(4*a))*(a*x^2+1)^(b/(4*a)))
 879                +gauss_b(sqrt(-4*a*c+b^2-2*a*b+a^2)/(2*a)+1/2,
 880                         1/2-(sqrt(-4*a*c+b^2-2*a*b+a^2)/(2*a)),b/(2*a),
 881                         1/2-(sqrt(-a)*x/2))
 882                 *(1-sqrt(-a)*x)^(b/(4*a))
 883                 /((-sqrt(-a)*x-1)^(b/(4*a))*(a*x^2+1)^(b/(4*a))))
 884          +%k1*(sqrt(-a)*gauss_a(sqrt(-4*a*c+b^2-2*a*b+a^2)/(2*a)+1/2,
 885                                 1/2-(sqrt(-4*a*c+b^2-2*a*b+a^2)/(2*a)),b/(2*a),
 886                                 1/2-(sqrt(-a)*x/2))*x*(1-sqrt(-a)*x)^(b/(4*a))
 887               /((-sqrt(-a)*x-1)^(b/(4*a))*(a*x^2+1)^(b/(4*a)))
 888               +gauss_a(sqrt(-4*a*c+b^2-2*a*b+a^2)/(2*a)+1/2,
 889                        1/2-(sqrt(-4*a*c+b^2-2*a*b+a^2)/(2*a)),b/(2*a),
 890                        1/2-(sqrt(-a)*x/2))
 891                *(1-sqrt(-a)*x)^(b/(4*a))
 892                /((-sqrt(-a)*x-1)^(b/(4*a))*(a*x^2+1)^(b/(4*a))))];
 893 [method,ode_check(eqn,ans[1])];
 894 [odelin,0];
 895 */
 896
 897 /* Kamke 2. 299  */
 898 (pn_(299),ans:contrib_ode(eqn:(a^2*x^2-1)*'diff(y,x,2)+2*a^2*x*'diff(y,x,1),y,x));
 899 [y=%k1*(log(a*x-1)/(2*a)-log(a*x+1)/(2*a))+%k2];
 900 ode_check(eqn,ans[1]);
 901 0;
 902 method;
 903 exact;
 904
 905 /* Kamke 2. 300  */
 906 (pn_(300),ans:contrib_ode(eqn:(a^2*x^2-1)*'diff(y,x,2)+2*a^2*x*'diff(y,x,1)-2*a^2*y,y,x));
 907 [y = gauss_b(-1,2,1,-((a*x-1)/2))*%k2+gauss_a(-1,2,1,-((a*x-1)/2))*%k1];
 908 [method,ode_check(eqn,ans[1])];
 909 [odelin,0];