share/contrib/diffequations/tests/rtestode_kamke_1_3.mac

   1 (load("contrib_ode"),0);
   2 0$
   3
   4 /* ODE tests - Equations 201-300
   5
   6   Reference:
   7     E Kamke, Differentialgleichungen Losungsmethoden und Losungen,
   8     Vol 1, Geest & Portig, Leipzig, 1961
   9
  10     E. S. Cheb-Terrab, T. Koloknikov,  First Order ODEs,
  11     Symmetries and Linear Transformations, European Journal of
  12     Applied Mathematics, Vol. 14, No. 2, pp. 231-246 (2003).
  13     (http://lie.uwaterloo.ca/papers/ode_iv.pdf)
  14
  15 */
  16 /* Don't kill(all); It messes up trigsimp */
  17
  18 /* Print ode number*/
  19 (pn_(n_):=print("Kamke ODE 1.",n_),true);
  20 true;
  21
  22 /*  201  */
  23 (pn_(201),ans:contrib_ode(eqn:2*f(x)*'diff(y,x,1)+2*f(x)*y^2-'diff(f(x),x,1)*y-2*f(x)^2,y,x));
  24 [y=sqrt(f(x))*(%c*sinh('integrate(sqrt(f(x)),x))+%i*cosh('integrate(sqrt(f(x)),x)))/(%i*sinh('integrate(sqrt(f(x)),x))+%c*cosh('integrate(sqrt(f(x)),x)))];
  25 [method,ode_check(eqn,ans[1])];
  26 [riccati,0];
  27
  28 /*  202  */
  29 /* This equation too general - E S Cheb-Terrab and T Kolokolnikov */
  30 /* (pn_( 202 ),ans:contrib_ode(eqn: f(x)*'diff(y,x,1)+g(x)*tg(y)+h(x) ,y,x)); */
  31
  32 /*  203  */
  33 (pn_(203),ans:contrib_ode(eqn:y*'diff(y,x,1)+y+x^3,y,x));
  34 false;
  35
  36 /*  204  */
  37 assume(a^2>4);
  38 [a^2>4];
  39 (pn_(204),ans:contrib_ode(eqn:y*'diff(y,x,1)+a*y+x,y,x));
  40 [%c*x=%e^-(((sqrt(a^2-4)*log((y^2+a*x*y+x^2)/x^2)-a*log(-((-2*y+sqrt(a^2-4)*x-a*x)/(2*y+sqrt(a^2-4)*x+a*x))))/(2*sqrt(a^2-4))))];
  41 method;
  42 homogeneous;
  43 forget(a^2>4);
  44 [a^2>4];
  45
  46 /*  205  */
  47 /* This equation too general - E S Cheb-Terrab and T Kolokolnikov */
  48 /* (pn_( 205 ),ans:contrib_ode(eqn: y*'diff(y,x,1)+a*y+b*x^n+(a^2-1)*x/4 ,y,x)); */
  49
  50 /*  206  */
  51 /* This equation too general - E S Cheb-Terrab and T Kolokolnikov */
  52 /* (pn_( 206 ),ans:contrib_ode(eqn: y*'diff(y,x,1)+a*y+b*%e^x-2*a ,y,x)); */
  53
  54 /*  207  */
  55 (pn_(207),ans:contrib_ode(eqn:y*'diff(y,x,1)+y^2+4*x*(x+1),y,x));
  56 [(%e^(2*x)*y^2+4*x^2*%e^(2*x))/2=%c];
  57 [method,ode_check(eqn,ans[1])];
  58 [exact,0];
  59
  60 /*  208  */
  61 (pn_(208),ans:contrib_ode(eqn:y*'diff(y,x,1)+a*y^2-b*cos(x+c),y,x));
  62 [((4*a^2+1)*%e^(2*a*x)*y^2-2*b*%e^(2*a*x)*sin(x+c)-4*a*b*%e^(2*a*x)*cos(x+c))/(8*a^2+2)=%c];
  63 [method,ode_check(eqn,ans[1])];
  64 [exact,0];
  65
  66 /*  209  */
  67 (pn_(209),ans:contrib_ode(eqn:y*'diff(y,x,1)-sqrt(a*y^2+b),y,x));
  68 [sqrt(a*y^2+b)/a=x+%c];
  69 [method,ode_check(eqn,ans[1])];
  70 [separable,0];
  71
  72 /*  210  */
  73 (pn_(210),ans:contrib_ode(eqn:y*'diff(y,x,1)+x*y^2-4*x,y,x));
  74 [-((log(y+2)+log(y-2))/2)=x^2/2+%c];
  75 [method,ode_check(eqn,ans[1])];
  76 [separable,0];
  77
  78 /*  211  */
  79 (pn_(211),ans:contrib_ode(eqn:y*'diff(y,x,1)-x*%e^(x/y),y,x));
  80 [%c*x=%e^'integrate(x*y/(x^2*%e^(x/y)-y^2),y/x)];
  81 method;
  82 homogeneous;
  83
  84 /*  212  */
  85 /* This equation presents a problem - crashes ode_contrib */
  86 /* (pn_( 212 ),ans:contrib_ode(eqn: g(x)*f(y^2+x^2)+y*'diff(y,x,1)+x ,y,x)); */
  87
  88 /* Abel equations of second kind */
  89 (pn_(213),ans:contrib_ode(eqn:(y+1)*'diff(y,x)=y+x,y,x));
  90 [-((log((2*(x-1)/(y+1)-sqrt(5)+1)/(2*(x-1)/(y+1)+sqrt(5)+1))+sqrt(5)*log((x-1)/(y+1)+(x-1)^2/(y+1)^2-1)-2*sqrt(5)*log((x-1)/(y+1)))/(2*sqrt(5)))=log(x-1)+%c];
  91 [method,ode_check(eqn,ans[1])];
  92 [abel2,0];
  93
  94 (pn_(214),ans:contrib_ode(eqn:(y+x-1)*'diff(y,x)-y+2*x+3=0,y,x));
  95 [-((2*atan((1-(3*x+2)/(y+x-1))/sqrt(2))+sqrt(2)*log(-(2*(3*x+2)/(y+x-1))+(3*x+2)^2/(y+x-1)^2+3)-(2*sqrt(2)*log(-((3*x+2)/(2*(y+x-1))))))/(6*sqrt(2)))=log(3*x+2)/3+%c];
  96 [method,ode_check(eqn,ans[1])];
  97 [abel2,0];
  98
  99 (pn_(215),ans:contrib_ode(eqn:(y+2*x-2)*'diff(y,x)-y+x+1=0,y,x),0);
 100 0$
 101 /*
 102 [-((6*atan((3-2*(3*x-1)/(y+2*x-2))/sqrt(3))+sqrt(3)*log(-((3*x-1)/(y+2*x-2))+(3*x-1)^2/(3*(y+2*x-2)^2)+1)-2*sqrt(3)*log(-((3*x-1)/(3*(y+2*x-2)))))/(6*sqrt(3)))=log(3*x-1)/3+%c];
 103  */
 104 [method,ode_check(eqn,ans[1])];
 105 [abel2,0];
 106
 107 (pn_(216),ans:contrib_ode(eqn:(y-2*x+1)*'diff(y,x)+y+x=0,y,x),0);
 108 0$
 109 /*
 110 [-((6*atan((2*(3*x-1)/(y-2*x+1)+3)/sqrt(3))+sqrt(3)*log((3*x-1)/(y-2*x+1)+(3*x-1)^2/(3*(y-2*x+1)^2)+1)-(2*sqrt(3)*log((3*x-1)/(3*(y-2*x+1)))))/(6*sqrt(3)))=log(3*x-1)/3+%c];
 111 */
 112 [method,ode_check(eqn,ans[1])];
 113 [abel2,0];
 114
 115 (pn_(217),ans:contrib_ode(eqn:(y-x^2)*'diff(y,x)=x,y,x));
 116 [(2*y-2*x^2-1)*%e^(2*y)/4 = %c];
 117 [method,ode_check(eqn,ans[1])];
 118 [exact,0];
 119
 120 (pn_(218),ans:contrib_ode(eqn:(y-x^2)*'diff(y,x)+4*x*y=0,y,x));
 121 [(2*y+2*x^2)/sqrt(y) = %c];
 122 [method,ode_check(eqn,ans[1])];
 123 [exact,0];
 124
 125 /*  219  */
 126 /* This equation too general - E S Cheb-Terrab and T Kolokolnikov */
 127 /* (pn_( 219 ),ans:contrib_ode(eqn: (y+g(x))*'diff(y,x,1)-f2(x)*y^2-f1(x)*y-f0(x) ,y,x)); */
 128
 129 (pn_(220),ans:contrib_ode(eqn:2*y*'diff(y,x)-x*y^2-x^3=0,y,x));
 130 [%e^-(x^2/2)*(y^2+x^2+2) = %c];
 131 [method,ode_check(eqn,ans[1])];
 132 [exact,0];
 133
 134 (pn_(221),ans:contrib_ode(eqn:(2*y+x+1)*'diff(y,x)-(2*y+x-1)=0,y,x));
 135 [-((2*y+x+1)*(
 136  -(4*(2*(x+1)+2*(1-x))*log(1-(2*(x+1)+2*(1-x))/(3*(2*y+x+1))) /(3*(2*y+x+1)))
 137  +(4*(2*(x+1)+2*(1-x))*log(-((2*(x+1)+2*(1-x))/(3*(2*y+x+1))))/(3*(2*y+x+1)))
 138  -4 )
 139  / (3*(2*(x+1)+2*(1-x))))
 140  =x+%c];
 141 [method,ode_check(eqn,ans[1])];
 142 [abel2,0];
 143
 144 /*  222  Why ask about ynew? */
 145 assume(ynew>-2);
 146 [ynew>-2];
 147 (pn_(222),ans:contrib_ode(eqn:(2*y+x+7)*'diff(y,x,1)-y+2*x+4,y,x));
 148 [-((atan((x+3)/(y+2))-log(y^2+4*y+x^2+6*x+13))/5)=%c];
 149 [method,ode_check(eqn,ans[1])];
 150 [exact,0];
 151 forget(ynew>-2);
 152 [ynew>-2];
 153
 154 /*  223  */
 155 (pn_(223),ans:contrib_ode(eqn:(2*y-x)*'diff(y,x,1)-y-2*x,y,x));
 156 [y^2-x*y-x^2=%c];
 157 [method,ode_check(eqn,ans[1])];
 158 [exact,0];
 159
 160 /*  224  */
 161 (pn_(224),ans:contrib_ode(eqn:(2*y-6*x)*'diff(y,x,1)-y+3*x+2,y,x));
 162 [(2*y-6*x)*(4*(2*(3*x+2)-6*x)*log((2*(3*x+2)-6*x)/(5*(2*y-6*x))+1)/(5*(2*y-6*x))-4*(2*(3*x+2)-6*x)*log((2*(3*x+2)-6*x)/(5*(2*y-6*x)))/(5*(2*y-6*x))-4)/(5*(2*(3*x+2)-6*x))=x+%c];
 163 [method,ode_check(eqn,ans[1])];
 164 [abel2,0];
 165
 166 /*  225  */
 167 (pn_(225),ans:contrib_ode(eqn:(4*y+2*x+3)*'diff(y,x,1)-2*y-x-1,y,x));
 168 [-((4*y+2*x+3) * (
 169    -( (2*(2*x+3)+4*(-x-1))*log(1-((2*(2*x+3)+4*(-x-1))/(4*(4*y+2*x+3))))  / (4*(4*y+2*x+3)) )
 170    +( (2*(2*x+3)+4*(-x-1))*log( -((2*(2*x+3)+4*(-x-1)) /(4*(4*y+2*x+3)))) / (4*(4*y+2*x+3)) )
 171    - 1 )
 172   )
 173   / (2*(2*(2*x+3)+4*(-x-1)))
 174  = x+%c];
 175 [method,ode_check(eqn,ans[1])];
 176 [abel2,0];
 177
 178 /*  226  */
 179 (pn_(226),ans:contrib_ode(eqn:(4*y-2*x-3)*'diff(y,x,1)+2*y-x-1,y,x));
 180 [(4*y-2*x-3)*((4*(-x-1)-2*(-2*x-3))*log((4*(-x-1)-2*(-2*x-3))/(4*(4*y-2*x-3))+1)/(4*(4*y-2*x-3))-(4*(-x-1)-2*(-2*x-3))*log((4*(-x-1)-2*(-2*x-3))/(4*(4*y-2*x-3)))/(4*(4*y-2*x-3))-1)/(2*(4*(-x-1)-2*(-2*x-3)))=x+%c];
 181 [method,ode_check(eqn,ans[1])];
 182 [abel2,0];
 183
 184 /*  227  */
 185 (pn_(227),ans:contrib_ode(eqn:(4*y-3*x-5)*'diff(y,x,1)-3*y+7*x+2,y,x));
 186 [(4*y^2+(-6*x-10)*y+7*x^2+4*x)/2=%c];
 187 [method,ode_check(eqn,ans[1])];
 188 [exact,0];
 189
 190 /*  228  */
 191 (pn_(228),ans:contrib_ode(eqn:(4*y+11*x-11)*'diff(y,x,1)-25*y-8*x+62,y,x));
 192 [(log(3-((25*(11*x-11)+4*(62-8*x))/(9*(4*y+11*x-11))))-3*log(1-((25*(11*x-11)+4*(62-8*x))/(9*(4*y+11*x-11))))+2*log(-((25*(11*x-11)+4*(62-8*x))/(36*(4*y+11*x-11)))))/18=log(9*x-1)/9+%c];
 193 [method,ode_check(eqn,ans[1])];
 194 [abel2,0];
 195
 196 /*  229  */
 197 (pn_(229),ans:contrib_ode(eqn:(12*y-5*x-8)*'diff(y,x,1)-5*y+2*x+3,y,x));
 198 [6*y^2+(-5*x-8)*y+x^2+3*x=%c];
 199 [method,ode_check(eqn,ans[1])];
 200 [exact,0];
 201
 202 /*  230  */
 203 (pn_(230),ans:contrib_ode(eqn:a*y*'diff(y,x,1)+b*y^2+f(x),y,x));
 204 [(2*'integrate(b*%e^(2*b*x/a)*y^2+%e^(2*b*x/a)*f(x),x)+(a*%e^(2*b*x/a)-2*b*'integrate(%e^(2*b*x/a),x))*y^2)/2=%c];
 205 method;
 206 exact;
 207
 208 /*  231  */
 209 /* This equation presents a problem - runs forever */
 210 /* (pn_( 231 ),ans:contrib_ode(eqn: gamma+(a*y+b*x+c)*'diff(y,x,1)+alpha*y+beta*x ,y,x)); */
 211
 212 /*  232  */
 213 (pn_(232),ans:contrib_ode(eqn:x*y*'diff(y,x,1)+y^2+x^2,y,x));
 214 [(2*x^2*y^2+x^4)/4=%c];
 215 [method,ode_check(eqn,ans[1])];
 216 [exact,0];
 217
 218 /*  233  */
 219 (pn_( 233 ),ans:contrib_ode(eqn: x*y*'diff(y,x,1)-y^2+a*x^3*cos(x) ,y,x));
 220 [(y^2+2*a*x^2*sin(x))/(2*x^2) = %c];
 221 [method,ode_check(eqn,ans[1])];
 222 [exact,0];
 223
 224 /*  234  */
 225 /* This equation too general - E S Cheb-Terrab and T Kolokolnikov */
 226 /* (pn_( 234 ),ans:contrib_ode(eqn: x*y*'diff(y,x,1)-y^2+x*y+x^3-2*x^2 ,y,x)); */
 227
 228 /*  235  */
 229 /* This equation too general - E S Cheb-Terrab and T Kolokolnikov */
 230 /* (pn_( 235 ),ans:contrib_ode(eqn: (x*y+a)*'diff(y,x,1)+b*y ,y,x)); */
 231
 232 /*  236  */
 233 (pn_( 236 ),ans:contrib_ode(eqn: x*(y+4)*'diff(y,x,1)-y^2-2*y-2*x ,y,x));
 234 [-((2*log(x-y)-log(-2*y+x-4)-log(x))/4) = %c];
 235 [method,ode_check(eqn,ans[1])];
 236 [lie,0];
 237
 238 /*  237  */
 239 /* This equation too general - E S Cheb-Terrab and T Kolokolnikov */
 240 /* (pn_( 237 ),ans:contrib_ode(eqn: x*(y+a)*'diff(y,x,1)+b*y+c*x ,y,x)); */
 241
 242 /*  238  */
 243 /* This equation presents a problem - runs forever */
 244 /* (pn_( 238 ),ans:contrib_ode(eqn: (x*(y+x)+a)*'diff(y,x,1)-y*(y+x)-b ,y,x)); */
 245
 246 /*  239  */
 247 (pn_(239),ans:contrib_ode(eqn:(x*y-x^2)*'diff(y,x,1)+y^2-3*x*y-2*x^2,y,x));
 248 [(x^2*y^2-2*x^3*y-x^4)/2=%c];
 249 [method,ode_check(eqn,ans[1])];
 250 [exact,0];
 251
 252 /*  240  */
 253 (pn_(240),ans:contrib_ode(eqn:2*x*y*'diff(y,x,1)-y^2+a*x,y,x));
 254 [(y^2+a*x*log(x))/x=%c];
 255 [method,ode_check(eqn,ans[1])];
 256 [exact,0];
 257
 258 /*  241  */
 259 (pn_(241),ans:contrib_ode(eqn:2*x*y*'diff(y,x,1)-y^2+a*x^2,y,x));
 260 [(y^2+a*x^2)/x=%c];
 261 [method,ode_check(eqn,ans[1])];
 262 [exact,0];
 263
 264 /*  242  */
 265 (pn_(242),ans:contrib_ode(eqn:2*x*y*'diff(y,x,1)+2*y^2+1,y,x));
 266 [-log(2*y^2+1)/2=log(x)+%c];
 267 [method,ode_check(eqn,ans[1])];
 268 [separable,0];
 269
 270 /*  243  */
 271 (pn_(243),ans:contrib_ode(eqn:x*(2*y+x-1)*'diff(y,x,1)-y*(y+2*x+1),y,x));
 272 [-log(y)+3*log(-y+x-1)-log(x)=%c];
 273 [method,ode_check(eqn,ans[1])];
 274 [lie,0];
 275
 276 /*  244  */
 277 (pn_(244),ans:contrib_ode(eqn:x*(2*y-x-1)*'diff(y,x,1)+(-y+2*x-1)*y,y,x));
 278 [3*log(y+x+1)-log(y)-log(x)=%c];
 279 [method,ode_check(eqn,ans[1])];
 280 [lie,0];
 281
 282 /*  245  */
 283 (pn_(245),ans:contrib_ode(eqn:(2*x*y+4*x^3)*'diff(y,x,1)+y^2+112*x^2*y,y,x));
 284 [x=%c*%e^-((11*log((y+24*x^2)/x^2)+log(y/x^2))/30)];
 285 method;
 286 genhom;
 287
 288 /*  246  */
 289 (pn_(246),ans:contrib_ode(eqn:x*(3*y+2*x)*'diff(y,x,1)+3*(y+x)^2,y,x));
 290 [(6*x^2*y^2+8*x^3*y+3*x^4)/4=%c];
 291 [method,ode_check(eqn,ans[1])];
 292 [exact,0];
 293
 294 /*  247  */
 295 (pn_(247),ans:contrib_ode(eqn:(3*x+2)*(y-2*x-1)*'diff(y,x,1)-y^2+x*y-7*x^2-9*x-3,y,x));
 296 [(2*log(y+x+1)+log(-2*y+7*x+4)-log(3*x+2))/6=%c];
 297 [method,ode_check(eqn,ans[1])];
 298 [lie,0];
 299
 300 /*  248  */
 301 /* This equation presents a problem - runs forever */
 302 /* (pn_( 248 ),ans:contrib_ode(eqn: (6*x*y+x^2+3)*'diff(y,x,1)+3*y^2+2*x*y+2*x ,y,x)); */
 303
 304 /*  249  */
 305 /* This equation presents a problem - runs forever */
 306 /* (pn_( 249 ),ans:contrib_ode(eqn: (a*x*y+b*x^n)*'diff(y,x,1)+alpha*y^3+beta*y^2 ,y,x)); */
 307
 308 /*  250  */
 309 /* This equation too general - E S Cheb-Terrab and T Kolokolnikov */
 310 /* (pn_( 250 ),ans:contrib_ode(eqn: gamma+(B*x*y+b*y+A*x^2+a*x+c)*'diff(y,x,1)+A*x*y+beta*y-B*g(x)^2+alpha*x ,y,x)); */
 311
 312 /*  251  */
 313 (pn_(251),ans:contrib_ode(eqn:(x^2*y-1)*'diff(y,x,1)+x*y^2-1,y,x));
 314 [(x^2*y^2-2*y-2*x)/2=%c];
 315 [method,ode_check(eqn,ans[1])];
 316 [exact,0];
 317
 318 /*  252  */
 319 (pn_(252),ans:contrib_ode(eqn:(x^2*y-1)*'diff(y,x,1)-x*y^2+1,y,x));
 320 [-((log(-3*x^2*y+x^3+2)-3*log(x-y))/6)=%c];
 321 [method,ode_check(eqn,ans[1])];
 322 [lie,0];
 323
 324 /*  253  */
 325 /* This equation too general - E S Cheb-Terrab and T Kolokolnikov */
 326 /* (pn_( 253 ),ans:contrib_ode(eqn: (x^2*y-1)*'diff(y,x,1)+8*(x*y^2-1) ,y,x)); */
 327
 328 /*  254  */
 329 (pn_(254),ans:contrib_ode(eqn:x*(x*y-2)*'diff(y,x,1)+x^2*y^3+x*y^2-2*y,y,x));
 330 [x=%c*%e^((x*y-1)/(x^2*y^2))];
 331 map(log,ans[1]/%c);
 332 log(x/%c)=(x*y-1)/(x^2*y^2);
 333 [method,ode_check(eqn,%)];
 334 [genhom,0];
 335
 336 /*  255  */
 337 (pn_(255),ans:contrib_ode(eqn:x*(x*y-3)*'diff(y,x,1)+x*y^2-y,y,x));
 338 [x=%c*%e^((3*log(x*y)-x*y)/2)];
 339 method;
 340 genhom;
 341
 342 /*  256  */
 343 (pn_(256),ans:contrib_ode(eqn:x^2*(y-1)*'diff(y,x,1)+(x-1)*y,y,x));
 344 [log(y)-y=(x*log(x)+1)/x+%c];
 345 [method,ode_check(eqn,ans[1])];
 346 [separable,0];
 347
 348 /*  257  */
 349 (pn_(257),ans:contrib_ode(eqn:x*(x*y+x^4-1)*'diff(y,x,1)-y*(x*y-x^4-1),y,x));
 350 false;
 351
 352 /*  258  */
 353 (pn_(258),ans:contrib_ode(eqn:2*x^2*y*'diff(y,x,1)+y^2-2*x^3-x^2,y,x));
 354 [%e^-(1/x)*(y^2+(-gamma_incomplete(-1,1/x)-2*gamma_incomplete(-2,1/x))*%e^(1/x))=%c];
 355 [method,ode_check(eqn,ans[1])];
 356 [exact,0];
 357
 358 /*  259  */
 359 (pn_(259),ans:contrib_ode(eqn:2*x^2*y*'diff(y,x,1)-y^2-x^2*%e^(x-1/x),y,x));
 360 [%e^(1/x)*y^2-%e^x=%c];
 361 [method,ode_check(eqn,ans[1])];
 362 [exact,0];
 363
 364 /*  260  */
 365 (pn_(260),ans:contrib_ode(eqn:(2*x^2*y+x)*'diff(y,x,1)-x^2*y^3+2*x*y^2+y,y,x));
 366 [x=%c*%e^-((4*x*y+1)/(2*x^2*y^2))];
 367 map(log,ans[1]/%c);
 368 log(x/%c)=-((4*x*y+1)/(2*x^2*y^2));
 369 [method,ode_check(eqn,%)];
 370 [genhom,0];
 371
 372 /*  261  */
 373 (pn_(261),ans:contrib_ode(eqn:(2*x^2*y-x)*'diff(y,x,1)-2*x*y^2-y,y,x));
 374 [x=%c*%e^((2*x*y*log(x*y)+1)/(4*x*y))];
 375  map(log,ans[1]/%c);
 376 log(x/%c)=(2*x*y*log(x*y)+1)/(4*x*y);
 377 [method,ode_check(eqn,%)];
 378 [genhom,0];
 379
 380 /*  262  */
 381 (pn_(262),ans:contrib_ode(eqn:(2*x^2*y-x^3)*'diff(y,x,1)+y^3-4*x*y^2+2*x^3,y,x));
 382 [%c*x=%e^((log((y+x)/x)+log((y-x)/x)-2*log((y-2*x)/x))/2)];
 383 method;
 384 homogeneous;
 385
 386 /*  263  */
 387 (pn_(263),ans:contrib_ode(eqn:y*'diff(y,x,1)+3*x^2*y^2+2*x^3+7,y,x));
 388 [(3*2^(1/3)*%e^(2*x^3)*y^2-2*gamma_incomplete(4/3,-2*x^3)+14*gamma_incomplete(1/3,-2*x^3))
 389    /(6*2^(1/3))=%c];
 390 [method,ode_check(eqn,ans[1])];
 391 [exact,0];
 392
 393 /*  264  */
 394 (pn_(264),ans:contrib_ode(eqn:2*x*(x^3*y+1)*'diff(y,x,1)+y*(3*x^3*y-1),y,x));
 395 [x=%c*%e^((8*log(3*x^3*y+7)+6*log(x^3*y))/21)];
 396 method;
 397 genhom;
 398
 399 /*  265  */
 400 /* This equation too general - E S Cheb-Terrab and T Kolokolnikov */
 401 /* (pn_( 265 ),ans:contrib_ode(eqn: (x^(n*(n+1))*y-1)*'diff(y,x,1)+2*(n+1)^2*x^(n-1)*(x^n^2*y^2-1) ,y,x)); */
 402
 403 /*  266  */
 404 (pn_( 266 ),ans:contrib_ode(eqn: sqrt(x^2+1)*(y-x)*'diff(y,x,1)-a*(y^2+1)^(3/2) ,y,x));
 405 false;
 406
 407 /*  267  */
 408 (pn_(267),ans:contrib_ode(eqn:sin(x)^2*y*'diff(y,x,1)+cos(x)*sin(x)*y^2-1,y,x));
 409 [(sin(x)^2*y^2-2*x)/2=%c];
 410 [method,ode_check(eqn,ans[1])];
 411 [exact,0];
 412
 413 /*  268  */
 414 (pn_(268),ans:contrib_ode(eqn:f(x)*y*'diff(y,x,1)+g(x)*y^2+h(x),y,x));
 415 [%e^-('integrate(('diff(f(x),x,1)-2*g(x))/f(x),x))*(2*%e^('integrate(('diff(f(x),x,1)-2*g(x))/f(x),x))*'integrate(%e^-('integrate(('diff(f(x),x,1)-2*g(x))/f(x),x))*(g(x)*y^2+h(x)),x)+(f(x)-2*%e^('integrate(('diff(f(x),x,1)-2*g(x))/f(x),x))*'integrate(g(x)*%e^-'integrate(('diff(f(x),x,1)-2*g(x))/f(x),x),x))*y^2)/2=%c];
 416 method;
 417 exact;
 418
 419 /*  269  */
 420 /* This equation too general - E S Cheb-Terrab and T Kolokolnikov */
 421 /* (pn_( 269 ),ans:contrib_ode(eqn: (bessel_i(1,x)*%e^-x*y+bessel_i(0,x)*%e^-x)*'diff(y,x,1)-f3(x)*y^3-f2(x)*y^2-f1(x)*y-f0(x) ,y,x)); */
 422
 423 /*  270  */
 424 (pn_(270),ans:contrib_ode(eqn:(y^2-x)*'diff(y,x,1)-y+x^2,y,x));
 425 [(y^3-3*x*y+x^3)/3=%c];
 426 [method,ode_check(eqn,ans[1])];
 427 [exact,0];
 428
 429 /*  271  */
 430 (pn_(271),ans:contrib_ode(eqn:(y^2+x^2)*'diff(y,x,1)+2*x*(y+2*x),y,x));
 431 [(y^3+3*x^2*y+4*x^3)/3=%c];
 432 [method,ode_check(eqn,ans[1])];
 433 [exact,0];
 434
 435 /*  272  */
 436 (pn_(272),ans:contrib_ode(eqn:(y^2+x^2)*'diff(y,x,1)-y^2,y,x));
 437 [%c*x=%e^-((2*atan((2*y-x)/(sqrt(3)*x))+sqrt(3)*log(y/x))/sqrt(3))];
 438 map(log,ans[1]);
 439 log(%c*x)=-((2*atan((2*y-x)/(sqrt(3)*x))+sqrt(3)*log(y/x))/sqrt(3));
 440 [method,ode_check(eqn,%)];
 441 [homogeneous,0];
 442
 443 /*  273  */
 444 (pn_(273),ans:contrib_ode(eqn:(y^2+x^2+a)*'diff(y,x,1)+2*x*y,y,x));
 445 [(y^3+(3*x^2+3*a)*y)/3=%c];
 446 [method,ode_check(eqn,ans[1])];
 447 [exact,0];
 448
 449 /*  274  */
 450 (pn_(274),ans:contrib_ode(eqn:(y^2+x^2+a)*'diff(y,x,1)+2*x*y+x^2+b,y,x));
 451 [(y^3+(3*x^2+3*a)*y+x^3+3*b*x)/3=%c];
 452 [method,ode_check(eqn,ans[1])];
 453 [exact,0];
 454
 455 /*  275  */
 456 (pn_(275),ans:contrib_ode(eqn:(y^2+x^2+x)*'diff(y,x,1)-y,y,x));
 457 false;
 458
 459 /*  276  */
 460 (pn_(276),ans:contrib_ode(eqn:(y^2-x^2)*'diff(y,x,1)+2*x*y,y,x));
 461 [-y/(y^2+x^2)=%c];
 462 [method,ode_check(eqn,ans[1])];
 463 [exact,0];
 464
 465 /*  277  */
 466 (pn_(277),ans:contrib_ode(eqn:(y^2+x^4)*'diff(y,x,1)-4*x^3*y,y,x));
 467 [(y^2-x^4)/y=%c];
 468 [method,ode_check(eqn,ans[1])];
 469 [exact,0];
 470
 471 /*  278  */
 472 (pn_(278),ans:contrib_ode(eqn:(y^2+4*sin(x))*'diff(y,x,1)-cos(x),y,x));
 473 [-((8*y^2+4*y+32*sin(x)+1)*%e^-(4*y)/32)=%c];
 474 [method,ode_check(eqn,ans[1])];
 475 [exact,0];
 476
 477 /*  279  */
 478 (pn_( 279 ),ans:contrib_ode(eqn: (y^2+2*y+x)*'diff(y,x,1)+y^2*(y+x)^2+y*(y+1) ,y,x));
 479 false;
 480
 481 /*  280  */
 482 (pn_(280),ans:contrib_ode(eqn:(y+x)^2*'diff(y,x,1)-a^2,y,x));
 483 [a*atan((y+x)/a)-y=%c];
 484 [method,ode_check(eqn,ans[1])];
 485 [lie,0];
 486
 487 /*  281  */
 488 (pn_(281),ans:contrib_ode(eqn:(y^2+2*x*y-x^2)*'diff(y,x,1)-y^2+2*x*y+x^2,y,x));
 489 [-((y+x)/(2*y^2+2*x^2))=%c];
 490 [method,ode_check(eqn,ans[1])];
 491 [exact,0];
 492
 493 /*  282  */
 494 (pn_(282),ans:contrib_ode(eqn:(y+3*x-1)^2*'diff(y,x,1)-(2*y-1)*(4*y+6*x-3),y,x));
 495 [(log(3*y+3*x-2)-3*log(2*y-1)+3*log(3*x-y))/6=%c];
 496 [method,ode_check(eqn,ans[1])];
 497 [lie,0];
 498
 499 /*  283  */
 500 (pn_(283),ans:contrib_ode(eqn:3*(y^2-x^2)*'diff(y,x,1)+2*y^3-6*x*(x+1)*y-3*%e^x,y,x));
 501 [%e^(2*x)*y^3-3*x^2*%e^(2*x)*y-%e^(3*x)=%c];
 502 [method,ode_check(eqn,ans[1])];
 503 [exact,0];
 504
 505 /*  284  */
 506 (pn_(284),ans:contrib_ode(eqn:(4*y^2+x^2)*'diff(y,x,1)-x*y,y,x));
 507 [(8*y^2*log(y)-x^2)/(2*y^2)=%c];
 508 [method,ode_check(eqn,ans[1])];
 509 [exact,0];
 510
 511 /*  285  */
 512 (pn_(285),ans:contrib_ode(eqn:(4*y^2+2*x*y+3*x^2)*'diff(y,x,1)+y^2+6*x*y+2*x^2,y,x));
 513 [(4*y^3+3*x*y^2+9*x^2*y+2*x^3)/3=%c];
 514 [method,ode_check(eqn,ans[1])];
 515 [exact,0];
 516
 517 /*  286  */
 518 (pn_(286),ans:contrib_ode(eqn:(2*y-3*x+1)^2*'diff(y,x,1)-(3*y-2*x-4)^2,y,x));
 519 [(5*log(-y+4*x-6)+5*log(-4*y+x+9)-log(-5*y+5*x+3))/45=%c];
 520 [method,ode_check(eqn,ans[1])];
 521 [lie,0];
 522
 523 /*  287  */
 524 (pn_(287),ans:contrib_ode(eqn:(2*y-4*x+1)^2*'diff(y,x,1)-(y-2*x)^2,y,x));
 525 [-((4*sqrt(2)*log(7*y^2+(8-28*x)*y+28*x^2-16*x+2)+9*log((7*y-14*x+sqrt(2)+4)/(7*y-14*x-sqrt(2)+4))-56*sqrt(2)*y+14*sqrt(2)*x)/(98*sqrt(2)))=%c];
 526 [method,ode_check(eqn,ans[1])];
 527 [lie,0];
 528
 529 /*  288  */
 530 (pn_(288),ans:contrib_ode(eqn:(6*y^2-3*x^2*y+1)*'diff(y,x,1)-3*x*y^2+x,y,x));
 531 [(4*y^3-3*x^2*y^2+2*y+x^2)/2=%c];
 532 [method,ode_check(eqn,ans[1])];
 533 [exact,0];
 534
 535 /*  289  */
 536 (pn_(289),ans:contrib_ode(eqn:(6*y-x)^2*'diff(y,x,1)-6*y^2+2*x*y+a,y,x));
 537 [12*y^3-6*x*y^2+x^2*y+a*x=%c];
 538 [method,ode_check(eqn,ans[1])];
 539 [exact,0];
 540
 541 /*  290  */
 542 (pn_(290),ans:contrib_ode(eqn:(a*y^2+2*b*x*y+c*x^2)*'diff(y,x,1)+b*y^2+2*c*x*y+d*x^2,y,x));
 543 [(a*y^3+3*b*x*y^2+3*c*x^2*y+d*x^3)/3=%c];
 544 [method,ode_check(eqn,ans[1])];
 545 [exact,0];
 546
 547 /*  291  */
 548 (pn_( 291 ),ans:contrib_ode(eqn: (b*(beta*y+alpha*x)^2-beta*(b*y+a*x))*'diff(y,x,1)+a*(beta*y+alpha*x)^2-alpha*(b*y+a*x) ,y,x));
 549 false;
 550
 551 /*  292  */
 552 /* This equation presents a problem - runs forever */
 553 /* (pn_( 292 ),ans:contrib_ode(eqn: (gamma+alpha*y+beta*x)^2+(a*y+b*x+c)^2*'diff(y,x,1) ,y,x)); */
 554
 555 /*  293  */
 556 (pn_(293),ans:contrib_ode(eqn:x*(y^2-3*x)*'diff(y,x,1)+2*y^3-5*x*y,y,x));
 557 [x=%c*%e^((2*log((5*y^2-13*x)/x)-30*log(y/sqrt(x)))/65)];
 558 method;
 559 genhom;
 560
 561 /*  294  */
 562 (pn_(294),ans:contrib_ode(eqn:x*(y^2+x^2-a)*'diff(y,x,1)-y*(y^2+x^2+a),y,x));
 563 [(log(-y^2+x^2-a)-log(y)-log(x))/a=%c];
 564 [method,ode_check(eqn,ans[1])];
 565 [lie,0];
 566
 567 /*  295  */
 568 (pn_(295),ans:contrib_ode(eqn:x*(y^2+x*y-x^2)*'diff(y,x,1)-y^3+x*y^2+x^2*y,y,x));
 569 [%c*x=%e^-((x*y*log(y/x)+y^2+x^2)/(2*x*y))];
 570 method;
 571 homogeneous;
 572
 573 /*  296  */
 574 /* This equation presents a problem - runs forever */
 575 /* (pn_( 296 ),ans:contrib_ode(eqn: x*(y^2+x^2*y+x^2)*'diff(y,x,1)-2*y^3-2*x^2*y^2+x^4 ,y,x)); */
 576
 577 /*  297  */
 578 (pn_(297),ans:contrib_ode(eqn:2*x*(y^2+5*x^2)*'diff(y,x,1)+y^3-x^2*y,y,x));
 579 [%c*x=%e^((2*log((y^2+3*x^2)/x^2)-10*log(y/x))/9)];
 580 method;
 581 homogeneous;
 582
 583 /*  298  */
 584 (pn_(298),ans:contrib_ode(eqn:3*x*y^2*'diff(y,x,1)+y^3-2*x,y,x));
 585 [x*y^3-x^2=%c];
 586 [method,ode_check(eqn,ans[1])];
 587 [exact,0];
 588
 589 /*  299  */
 590 (pn_(299),ans:contrib_ode(eqn:(3*x*y^2-x^2)*'diff(y,x,1)+y^3-2*x*y,y,x));
 591 [x*y^3-x^2*y=%c];
 592 [method,ode_check(eqn,ans[1])];
 593 [exact,0];
 594
 595 /*  300  */
 596 (pn_(300),ans:contrib_ode(eqn:6*x*y^2*'diff(y,x,1)+2*y^3+x,y,x));
 597 [(4*x*y^3+x^2)/2=%c];
 598 [method,ode_check(eqn,ans[1])];
 599 [exact,0];