share/contrib/diffequations/tests/rtestode_kamke_1_4.mac

   1 (load("contrib_ode"),0);
   2 0$
   3
   4 /* ODE tests - Equations 1.301-1.400
   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 /*  301  */
  23 (pn_(301),ans:contrib_ode(eqn:(6*x*y^2+x^2)*'diff(y,x,1)-y*(3*y^2-x),y,x));
  24 [x=%c*%e^-((2*x*log(y/sqrt(x))+6*y^2)/(3*x))];
  25 method;
  26 genhom;
  27
  28 /*  302  */
  29 (pn_(302),ans:contrib_ode(eqn:(x^2*y^2+x)*'diff(y,x,1)+y,y,x));
  30 [x=%c*(x*y^2-1)^2/(x*y^2)];
  31 method;
  32 genhom;
  33
  34 /*  303  */
  35 (pn_(303),ans:contrib_ode(eqn:x*(x*y-1)^2*'diff(y,x,1)+y*(x^2*y^2+1),y,x));
  36 [x=%c*%e^((2*x*y*log(x*y)-x^2*y^2+1)/(2*x*y))];
  37 method;
  38 genhom;
  39
  40 /*  304  */
  41 (pn_(304),ans:contrib_ode(eqn:(10*x^3*y^2+x^2*y+2*x)*'diff(y,x,1)+5*x^2*y^3+x*y^2,y,x));
  42 [x=%c*%e^((sqrt(10)*log(5*x^2*y^2+2)+2*atan(5*x*y/sqrt(10))+2*sqrt(10)*log(x*y))/(2*sqrt(10)))];
  43 method;
  44 genhom;
  45
  46 /*  305  */
  47 (pn_(305),ans:contrib_ode(eqn:(y^3-3*x)*'diff(y,x,1)-3*y+x^2,y,x));
  48 [(3*y^4-36*x*y+4*x^3)/12=%c];
  49 [method,ode_check(eqn,ans[1])];
  50 [exact,0];
  51
  52 /*  306  */
  53 (pn_(306),ans:contrib_ode(eqn:(y^3-x^3)*'diff(y,x,1)-x^2*y,y,x));
  54 [(y^6-2*x^3*y^3)/6=%c];
  55 [method,ode_check(eqn,ans[1])];
  56 [exact,0];
  57
  58 /*  307  */
  59 (pn_(307),ans:contrib_ode(eqn:y*(y^2+x^2+a)*'diff(y,x,1)+x*(y^2+x^2-a),y,x));
  60 [(y^4+(2*x^2+2*a)*y^2+x^4-2*a*x^2)/4=%c];
  61 [method,ode_check(eqn,ans[1])];
  62 [exact,0];
  63
  64 /*  308  */
  65 (pn_(308),ans:contrib_ode(eqn:2*y^3*'diff(y,x,1)+x*y^2,y,x));
  66 [-y^2=x^2/2+%c];
  67 [method,ode_check(eqn,ans[1])];
  68 [separable,0];
  69
  70 /*  309  */
  71 (pn_(309),ans:contrib_ode(eqn:(2*y^3+y)*'diff(y,x,1)-2*x^3-x,y,x));
  72 [(4*y^4+4*y^2+1)/8=(4*x^4+4*x^2+1)/8+%c];
  73 [method,ode_check(eqn,ans[1])];
  74 [separable,0];
  75
  76 /*  310  */
  77 (pn_(310),ans:contrib_ode(eqn:(2*y^3+5*x^2*y)*'diff(y,x,1)+5*x*y^2+x^3,y,x));
  78 [(2*y^4+10*x^2*y^2+x^4)/4=%c];
  79 [method,ode_check(eqn,ans[1])];
  80 [exact,0];
  81
  82 /*  311  */
  83 (pn_(311),ans:contrib_ode(eqn:(20*y^3-3*x*y^2+6*x^2*y+3*x^3)*'diff(y,x,1)-y^3+6*x*y^2+9*x^2*y+4*x^3,y,x));
  84 [5*y^4-x*y^3+3*x^2*y^2+3*x^3*y+x^4=%c];
  85 [method,ode_check(eqn,ans[1])];
  86 [exact,0];
  87
  88 /*  312  */
  89 /* This equation presents a problem - runs forever */
  90 /* (pn_( 312 ),ans:contrib_ode(eqn: (y^2/b+x^2/a)*(y*'diff(y,x,1)+x)+(a-b)*(y*'diff(y,x,1)-x)/(b+a) ,y,x)); */
  91
  92 /*  313  */
  93 /* This equation presents a problem - runs forever */
  94 /* (pn_( 313 ),ans:contrib_ode(eqn: (2*a*y^3+3*a*x*y^2-b*x^3+c*x^2)*'diff(y,x,1)-a*y^3+c*y^2+3*b*x^2*y+2*b*x^3 ,y,x)); */
  95
  96 /*  314  */
  97 (pn_(314),ans:contrib_ode(eqn:x*y^3*'diff(y,x,1)+y^4-x*sin(x),y,x));
  98 [(x^4*y^4+(96*x-16*x^3)*sin(x)+(4*x^4-48*x^2+96)*cos(x))/4=%c];
  99 [method,ode_check(eqn,ans[1])];
 100 [exact,0];
 101
 102 /*  315  */
 103 (pn_(315),ans:contrib_ode(eqn:(2*x*y^3-x^4)*'diff(y,x,1)-y^4+2*x^3*y,y,x));
 104 [%c*x=x^2*y/((y+x)*(y^2-x*y+x^2))];
 105 method;
 106 homogeneous;
 107
 108 /*  316  */
 109 (pn_(316),ans:contrib_ode(eqn:(2*x*y^3+y)*'diff(y,x,1)+2*y^2,y,x));
 110 [(4*x*%e^(y^2/2)-gamma_incomplete(0,-y^2/2))/2=%c];
 111 [method,ode_check(eqn,ans[1])];
 112 [exact,0];
 113
 114 /*  317  */
 115 /* This equation presents a problem - runs forever */
 116 /* (pn_( 317 ),ans:contrib_ode(eqn: (2*x*y^3+x*y+x^2)*'diff(y,x,1)+y^2-x*y ,y,x)); */
 117
 118 /*  318  */
 119 (pn_(318),ans:contrib_ode(eqn:(3*x*y^3-4*x*y+y)*'diff(y,x,1)+y^2*(y^2-2),y,x));
 120 [(x*y^4+(1-2*x)*y^2-2)/sqrt(y^2-2)=%c];
 121 [method,ode_check(eqn,ans[1])];
 122 [exact,0];
 123
 124 /*  319  */
 125 (pn_(319),ans:contrib_ode(eqn:(7*x*y^3+y-5*x)*'diff(y,x,1)+y^4-5*y,y,x));
 126 [(10*x*y^7+2*y^5-100*x*y^4-25*y^2+250*x*y)/10=%c];
 127 [method,ode_check(eqn,ans[1])];
 128 [exact,0];
 129
 130 /*  320  */
 131 (pn_(320),ans:contrib_ode(eqn:(x^2*y^3+x*y)*'diff(y,x,1)-1,y,x));
 132 false;
 133
 134 /*  321  */
 135 /* This equation presents a problem - runs forever */
 136 /* (pn_( 321 ),ans:contrib_ode(eqn: (2*x^2*y^3+x^2*y^2-2*x)*'diff(y,x,1)-2*y-1 ,y,x)); */
 137
 138 /*  322  */
 139 (pn_(322),ans:contrib_ode(eqn:(10*x^2*y^3-3*y^2-2)*'diff(y,x,1)+5*x*y^4+x,y,x));
 140 [(5*x^2*y^4-2*y^3-4*y+x^2)/2=%c];
 141 [method,ode_check(eqn,ans[1])];
 142 [exact,0];
 143
 144 /*  323  */
 145 /* This equation presents a problem - runs forever */
 146 /* (pn_( 323 ),ans:contrib_ode(eqn: x*(a*x*y^3+c)*'diff(y,x,1)+y*(b*x^3*y+c) ,y,x)); */
 147
 148 /*  324  */
 149 /* This equation presents a problem - runs forever */
 150 /* (pn_( 324 ),ans:contrib_ode(eqn: (2*x^3*y^3-x)*'diff(y,x,1)+2*x^3*y^3-y ,y,x)); */
 151
 152 /*  325  */
 153 (pn_(325),ans:contrib_ode(eqn:y*(y^3-2*x^3)*'diff(y,x,1)+x*(2*y^3-x^3),y,x));
 154 [%c*x=%e^-(('integrate((8*x*y^3+9*x^2*y^2+12*x^3*y-x^4)/(y^4+x*y^3+3*x^2*y^2+x^3*y+x^4),y/x)-log((y-x)/x))/7)];
 155 method;
 156 homogeneous;
 157
 158 /*  326  */
 159 (pn_(326),ans:contrib_ode(eqn:y*((a*y+b*x)^3+b*x^3)*'diff(y,x,1)+x*((a*y+b*x)^3+a*y^3),y,x));
 160 [%c*x=%e^-((log((a^2*y^4+2*a*b*x*y^3+(b^2+a^2+1)*x^2*y^2+2*a*b*x^3*y+b^2*x^4)/x^4)-2*log((a*y+b*x)/x))/2)];
 161 method;
 162 homogeneous;
 163
 164 /*  327  */
 165 /* This equation presents a problem - runs forever */
 166 /* (pn_( 327 ),ans:contrib_ode(eqn: (x*y^4+2*x^2*y^3+2*y+x)*'diff(y,x,1)+y^5+y ,y,x)); */
 167
 168 /*  328  */
 169 (pn_(328),ans:contrib_ode(eqn:a*x^2*y^n*'diff(y,x,1)-2*x*'diff(y,x,1)+y,y,x));
 170 [x=%c*%e^((n*log((a*%e^(n*log(x^(1/n)*y))-n-2)/a)+2*n*log(x^(1/n)*y))/(n+2))];
 171 method;
 172 genhom;
 173
 174 /*  329  */
 175 (pn_(329),ans:contrib_ode(eqn:x^n*y^m*(a*x*'diff(y,x,1)+b*y)+alpha*x*'diff(y,x,1)+beta*y,y,x));
 176 [x=%c*%e^-(((a*beta-alpha*b)*m*log(((a*n-b*m)*%e^(m*log(x^(n/m)*y))+alpha*n-beta*m)/(a*n-b*m))+(alpha*b*m^2-a*alpha*m*n)*log(x^(n/m)*y))/(a*alpha*n^2+(-a*beta-alpha*b)*m*n+b*beta*m^2))];
 177 method;
 178 genhom;
 179
 180 /*  330  */
 181 /* This equation presents a problem - runs forever */
 182 /* (pn_( 330 ),ans:contrib_ode(eqn: 'diff(y,x,1)*(f(y+x)+1)+f(y+x) ,y,x)); */
 183
 184 /*  331  */
 185 /* This equation too general - E S Cheb-Terrab and T Kolokolnikov */
 186 /* (pn_( 331 ),ans:contrib_ode(eqn: ode[331] ,y,x)); */
 187
 188 /*  332  */
 189 (pn_(332),ans:contrib_ode(eqn:x*(sqrt(x*y)-1)*'diff(y,x,1)-y*(sqrt(x*y)+1),y,x));
 190 [x=%c*%e^((sqrt(x*y)*log(x*y)+2)/(2*sqrt(x*y)))];
 191 method;
 192 genhom;
 193
 194 /*  333  */
 195 /* This equation presents a problem - crashes ode_contrib */
 196 /* (pn_( 333 ),ans:contrib_ode(eqn: (2*x^(5/2)*y^(3/2)+x^2*y-x)*'diff(y,x,1)-x^(3/2)*y^(5/2)+x*y^2-y ,y,x)); */
 197
 198 /*  334  */
 199 /* This equation presents a problem - runs forever */
 200 /* (pn_( 334 ),ans:contrib_ode(eqn: (sqrt(y+x)+1)*'diff(y,x,1)+1 ,y,x)); */
 201
 202 /*  335  */
 203 (pn_(335),ans:contrib_ode(eqn:sqrt(y^2-1)*'diff(y,x,1)-sqrt(x^2-1),y,x));
 204 [(y*sqrt(y^2-1)-log(2*sqrt(y^2-1)+2*y))/2=(x*sqrt(x^2-1)-log(2*sqrt(x^2-1)+2*x))/2+%c];
 205 [method,ode_check(eqn,ans[1])];
 206 [separable,0];
 207
 208 /*  336  */
 209 (pn_(336),ans:contrib_ode(eqn:(sqrt(y^2+1)+a*x)*'diff(y,x,1)+a*y+sqrt(x^2+1),y,x));
 210 [(asinh(y)+y*sqrt(y^2+1)+2*a*x*y+asinh(x)+x*sqrt(x^2+1))/2=%c];
 211 [method,ode_check(eqn,ans[1])];
 212 [exact,0];
 213
 214 /*  337  */
 215 /* This equation presents a problem - runs forever */
 216 /* (pn_( 337 ),ans:contrib_ode(eqn: (sqrt(y^2+x^2)+x)*'diff(y,x,1)-y ,y,x)); */
 217
 218 /*  338  */
 219 /* This equation presents a problem - runs forever */
 220 /* (pn_( 338 ),ans:contrib_ode(eqn: (y*sqrt(y^2+x^2)+sin(alpha)*(y^2-x^2)-2*cos(alpha)*x*y)*'diff(y,x,1)+x*sqrt(y^2+x^2)+cos(alpha)*(y^2-x^2)+2*sin(alpha)*x*y ,y,x)); */
 221
 222 /*  339  */
 223 /* This equation presents a problem - runs forever */
 224 /* (pn_( 339 ),ans:contrib_ode(eqn: (x*sqrt(y^2+x^2+1)-y*(y^2+x^2))*'diff(y,x,1)-y*sqrt(y^2+x^2+1)-x*(y^2+x^2) ,y,x)); */
 225
 226 /*  340  CHECKME
 227  2008-02-24:  Now fails with "Expression too wide to be displayed */
 228 /* (pn_(340),ans:contrib_ode(eqn:(e1*(x+a)/(y^2+(x+a)^2)^(3/2)+e2*(x-a)/(y^2+(x-a)^2)^(3/2))*'diff(y,x,1)-y*(e1/(y^2+(x+a)^2)^(3/2)+e2/(y^2+(x-a)^2)^(3/2)),y,x));
 229 [-'integrate((sqrt(y^2+x^2+2*a*x+a^2)*(sqrt(y^2+x^2-2*a*x+a^2)*(y^4+(2*x^2+2*a^2)*y^2+x^4-2*a^2*x^2+a^4)*'integrate((sqrt(y^2+x^2+2*a*x+a^2)*(e2*y^7+8*a*e2*x*y^5+(-3*e2*x^4+4*a*e2*x^3+14*a^2*e2*x^2+4*a^3*e2*x-3*a^4*e2)*y^3+(-2*e2*x^6-4*a*e2*x^5+2*a^2*e2*x^4+8*a^3*e2*x^3+2*a^4*e2*x^2-4*a^5*e2*x-2*a^6*e2)*y)+sqrt(y^2+x^2-2*a*x+a^2)*(e1*y^7-8*a*e1*x*y^5+(-3*e1*x^4-4*a*e1*x^3+14*a^2*e1*x^2-4*a^3*e1*x-3*a^4*e1)*y^3+(-2*e1*x^6+4*a*e1*x^5+2*a^2*e1*x^4-8*a^3*e1*x^3+2*a^4*e1*x^2+4*a^5*e1*x-2*a^6*e1)*y))/(sqrt(y^2+x^2-2*a*x+a^2)*sqrt(y^2+x^2+2*a*x+a^2)*(y^8+(4*x^2+4*a^2)*y^6+(6*x^4+4*a^2*x^2+6*a^4)*y^4+(4*x^6-4*a^2*x^4-4*a^4*x^2+4*a^6)*y^2+x^8-4*a^2*x^6+6*a^4*x^4-4*a^6*x^2+a^8)),x)+(a*e2-e2*x)*y^3+(-e2*x^3-a*e2*x^2+a^2*e2*x+a^3*e2)*y)+sqrt(y^2+x^2-2*a*x+a^2)*((-e1*x-a*e1)*y^3+(-e1*x^3+a*e1*x^2+a^2*e1*x-a^3*e1)*y))/(sqrt(y^2+x^2-2*a*x+a^2)*sqrt(y^2+x^2+2*a*x+a^2)*(y^4+(2*x^2+2*a^2)*y^2+x^4-2*a^2*x^2+a^4)),y)-'integrate((sqrt(y^2+x^2-2*a*x+a^2)*(e2*y^6+(2*e2*x^2+4*a*e2*x+2*a^2*e2)*y^4+(e2*x^4+4*a*e2*x^3+6*a^2*e2*x^2+4*a^3*e2*x+a^4*e2)*y^2)+sqrt(y^2+x^2+2*a*x+a^2)*(e1*y^6+(2*e1*x^2-4*a*e1*x+2*a^2*e1)*y^4+(e1*x^4-4*a*e1*x^3+6*a^2*e1*x^2-4*a^3*e1*x+a^4*e1)*y^2))/(y^8+(4*x^2+4*a^2)*y^6+(6*x^4+4*a^2*x^2+6*a^4)*y^4+(4*x^6-4*a^2*x^4-4*a^4*x^2+4*a^6)*y^2+x^8-4*a^2*x^6+6*a^4*x^4-4*a^6*x^2+a^8),x)=%c];
 230 method;
 231 exact;
 232 */
 233
 234 /*  341  */
 235 (pn_(341),ans:contrib_ode(eqn:(x*%e^y+%e^x)*'diff(y,x,1)+%e^y+%e^x*y,y,x));
 236 [x*%e^y+%e^x*y=%c];
 237 [method,ode_check(eqn,ans[1])];
 238 [exact,0];
 239
 240 /*  342  */
 241 (pn_(342),ans:contrib_ode(eqn:x*(3*%e^(x*y)+2*%e^-(x*y))*(x*'diff(y,x,1)+y)+1,y,x));
 242 [%e^-(x*y)*(3*%e^(2*x*y)+log(x)*%e^(x*y)-2)=%c];
 243 [method,ode_check(eqn,ans[1])];
 244 [exact,0];
 245
 246 /*  343  */
 247 (pn_(343),ans:contrib_ode(eqn:(log(y)+x)*'diff(y,x,1)-1,y,x));
 248 [-%e^-y*(log(y)+gamma_incomplete(0,y)*%e^y+x)=%c];
 249 [method,ode_check(eqn,ans[1])];
 250 [exact,0];
 251
 252 /*  344  */
 253 (pn_(344),ans:contrib_ode(eqn:(log(y)+2*x-1)*'diff(y,x,1)-2*y,y,x));
 254 [-((log(y)+2*x)/y)=%c];
 255 [method,ode_check(eqn,ans[1])];
 256 [exact,0];
 257
 258 /*  345  */
 259 (pn_(345),ans:contrib_ode(eqn:x*(2*x^2*y*log(y)+1)*'diff(y,x,1)-2*y,y,x));
 260 [(2*x^2*y^2*log(y)-x^2*y^2+2*y)/(2*x^2)=%c];
 261 [method,ode_check(eqn,ans[1])];
 262 [exact,0];
 263
 264 /*  346  */
 265 /* This equation presents a problem - runs forever */
 266 /* (pn_( 346 ),ans:contrib_ode(eqn: x*'diff(y,x,1)*(y*log(x*y)+y-a*x)-y*(a*x*log(x*y)-y+a*x) ,y,x)); */
 267
 268 /*  347  */
 269 (pn_(347),ans:contrib_ode(eqn:(sin(x)+1)*sin(y)*'diff(y,x,1)+cos(x)*(cos(y)-1),y,x));
 270 [log(cos(y)-1)=log(sin(x)+1)+%c];
 271 [method,ode_check(eqn,ans[1])];
 272 [separable,0];
 273
 274 /*  348  */
 275 (pn_(348),ans:contrib_ode(eqn:(x*cos(y)+sin(x))*'diff(y,x,1)+sin(y)+cos(x)*y,y,x));
 276 [x*sin(y)+sin(x)*y=%c];
 277 [method,ode_check(eqn,ans[1])];
 278 [exact,0];
 279
 280 /*  349  */
 281 (pn_(349),ans:contrib_ode(eqn:2*x*sin(y/x)+x*'diff(y,x,1)*cot(y/x)-y*cot(y/x),y,x));
 282 [%c*x=%e^(1/(2*sin(y/x)))];
 283 solve(map(log,ans[1]),y);
 284 [y=x*asin(1/(2*log(%c*x)))];
 285 [method,ode_check(eqn,%[1])];
 286 [homogeneous,0];
 287
 288 /*  350  */
 289 (pn_(350),ans:contrib_ode(eqn:cos(y)*'diff(y,x,1)-cos(x)*sin(y)^2-sin(y),y,x));
 290 false;
 291
 292 /*  351  */
 293 /* This equation presents a problem - crashes ode_contrib */
 294 /* (pn_( 351 ),ans:contrib_ode(eqn: cos(y)*'diff(y,x,1)-sin(y)^3+x*cos(y)^2*sin(y) ,y,x)); */
 295
 296 /*  352  */
 297 (pn_(352),ans:contrib_ode(eqn:cos(y)*(cos(y)-sin(alpha)*sin(x))*'diff(y,x,1)+cos(x)*(cos(x)-sin(alpha)*sin(y)),y,x));
 298 [(sin(2*y)-4*sin(alpha)*sin(x)*sin(y)+2*y+sin(2*x)+2*x)/4=%c];
 299  [method,expand(exponentialize(ode_check(eqn,ans[1])))];
 300 [exact,0];
 301
 302 /*  353  */
 303 (pn_(353),ans:contrib_ode(eqn:x*cos(y)*'diff(y,x,1)+sin(y),y,x));
 304 [-log(sin(y))=log(x)+%c];
 305 [method,ode_check(eqn,ans[1])];
 306 [separable,0];
 307
 308 /*  354  */
 309 (pn_(354),ans:contrib_ode(eqn:(x*sin(y)-1)*'diff(y,x,1)+cos(y),y,x));
 310 [-((cos(y)*tan(y)-x)/cos(y))=%c];
 311 [method,ode_check(eqn,ans[1])];
 312 [exact,0];
 313
 314 /*  355  */
 315 (pn_(355),ans:contrib_ode(eqn:(x*cos(y)+cos(x))*'diff(y,x,1)+sin(y)-sin(x)*y,y,x));
 316 [x*sin(y)+cos(x)*y=%c];
 317 [method,ode_check(eqn,ans[1])];
 318 [exact,0];
 319
 320 /*  356  */
 321 (pn_(356),ans:contrib_ode(eqn:(x^2*cos(y)+2*sin(x)*y)*'diff(y,x,1)+2*x*sin(y)+cos(x)*y^2,y,x));
 322 [x^2*sin(y)+sin(x)*y^2=%c];
 323 [method,ode_check(eqn,ans[1])];
 324 [exact,0];
 325
 326 /*  357  */
 327 (pn_(357),ans:contrib_ode(eqn:x*log(x)*sin(y)*'diff(y,x,1)+cos(y)*(1-x*cos(y)),y,x));
 328 false;
 329
 330 /*  358  */
 331 (pn_(358),ans:contrib_ode(eqn:cos(x)*sin(y)*'diff(y,x,1)+sin(x)*cos(y),y,x));
 332 [log(cos(y))=%c-log(cos(x))];
 333 [method,ode_check(eqn,ans[1])];
 334 [separable,0];
 335
 336 /*  359  */
 337 (pn_(359),ans:contrib_ode(eqn:3*sin(x)*sin(y)*'diff(y,x,1)+5*cos(x)^4*y,y,x));
 338  [(3*%i*gamma_incomplete(0,%i*y)-3*%i*gamma_incomplete(0,-%i*y))/10
 339           = %c-(3*log(cos(x)+1)-3*log(cos(x)-1)-2*cos(x)^3-6*cos(x))/6]$
 340 [method,ode_check(eqn,ans[1])];
 341 [separable,0];
 342
 343 /*  360  */
 344 (pn_(360),ans:contrib_ode(eqn:'diff(y,x,1)*cos(a*y)-b*(1-c*cos(a*y))*sqrt(cos(a*y)^2+c*cos(a*y)-1),y,x));
 345 [-('integrate(cos(a*y)/((c*cos(a*y)-1)*sqrt(cos(a*y)^2+c*cos(a*y)-1)),y))/b=x+%c];
 346 [method,ode_check(eqn,ans[1])];
 347 [separable,0];
 348
 349 /*  361  */
 350 (pn_(361),ans:contrib_ode(eqn:'diff(y,x,1)*(cos(y+x)+x*sin(x*y)-sin(y))+cos(y+x)+y*sin(x*y)+cos(x),y,x));
 351 [sin(y+x)-cos(x*y)+cos(y)+sin(x)=%c];
 352 [method,ode_check(eqn,ans[1])];
 353 [exact,0];
 354
 355 /*  362  */
 356 (pn_(362),ans:contrib_ode(eqn:'diff(y,x,1)*(x^2*y*sin(x*y)-4*x)+x*y^2*sin(x*y)-y,y,x));
 357 [x=%c*%e^((4*log(x*y)+cos(x*y))/3)];
 358 method;
 359 genhom;
 360
 361 /*  363  */
 362 (pn_(363),ans:contrib_ode(eqn:(x*'diff(y,x,1)-y)*cos(y/x)^2+x,y,x));
 363 [(x*sin(2*y/x)+2*y+4*x*log(x))/(4*x)=%c];
 364 [method,expand(exponentialize(ode_check(eqn,ans[1])))];
 365 [exact,0];
 366
 367 /*  364  */
 368 (pn_(364),ans:contrib_ode(eqn:x*'diff(y,x,1)*(y*sin(y/x)-x*cos(y/x))-y*(y*sin(y/x)+x*cos(y/x)),y,x));
 369 [-x*y*cos(y/x)=%c];
 370 [method,ode_check(eqn,ans[1])];
 371 [exact,0];
 372
 373 /*  365  */
 374 /* This equation presents a problem - crashes ode_contrib */
 375 /* (pn_( 365 ),ans:contrib_ode(eqn: 'diff(y,x,1)*(y*f(y^2+x^2)-x)+x*f(y^2+x^2)+y ,y,x)); */
 376
 377 /*  366  */
 378 use_pdiff:true;
 379 true;
 380 (pn_(366),ans:contrib_ode(eqn:(a*y*'diff(y,x,1)+x)*f(a*y^2+x^2)-x*'diff(y,x,1)-y,y,x));
 381 ['integrate(a*y*f(a*y^2+x^2)-2*a*y*'integrate(x*pderivop(f,1)(a*y^2+x^2),x),y)+'integrate(x*f(a*y^2+x^2),x)-x*y=%c];
 382 method;
 383 exact;
 384 use_pdiff:false;
 385 false;
 386
 387 /*  367  */
 388 /* This equation presents a problem - crashes ode_contrib */
 389 /* (pn_( 367 ),ans:contrib_ode(eqn: (b*x*'diff(y,x,1)-a)*f(x^c*y)-x^a*y^b*(x*'diff(y,x,1)+c*y) ,y,x)); */
 390
 391 /*  368  */
 392 /* This equation presents a problem - runs forever */
 393 /* (pn_( 368 ),ans:contrib_ode(eqn: ('diff(y,x,1))^2+a*y+b*x^2 ,y,x)); */
 394
 395 /*  369  */
 396 assume(a>0);
 397 [a>0];
 398 (pn_(369),ans:contrib_ode(eqn:('diff(y,x,1))^2+y^2-a^2,y,x));
 399 [[x=asin(%t/abs(a))+%c,y=-sqrt(a^2-%t^2)],[x=%c-asin(%t/abs(a)),y=sqrt(a^2-%t^2)]];
 400 ans[1]:ans[1][2],solve(ans[1][1],%t);
 401 y=-sqrt(a^2-a^2*sin(x-%c)^2);
 402 ans[2]:ans[2][2],solve(ans[2][1],%t);
 403 y=sqrt(a^2-a^2*sin(x-%c)^2);
 404 [method,ode_check(eqn,ans[1]),ode_check(eqn,ans[2])];
 405 [lagrange,0,0];
 406 forget(a>0);
 407 [a>0];
 408
 409 /*  370  */
 410 /* This equation too general - E S Cheb-Terrab and T Kolokolnikov */
 411 /* (pn_( 370 ),ans:contrib_ode(eqn: ('diff(y,x,1))^2+y^2-f(x)^2 ,y,x)); */
 412
 413 /*  371  */
 414 /* This equation presents a problem - crashes ode_contrib */
 415 /* (pn_( 371 ),ans:contrib_ode(eqn: ('diff(y,x,1))^2-y^3+y^2 ,y,x)); */
 416
 417 /*  372  */
 418 /* This equation presents a problem - runs forever */
 419 /* (pn_( 372 ),ans:contrib_ode(eqn: ('diff(y,x,1))^2-4*y^3+a*y+b ,y,x)); */
 420
 421 /*  373  */
 422 /* This equation presents a problem - crashes ode_contrib */
 423 /* (pn_( 373 ),ans:contrib_ode(eqn: ('diff(y,x,1))^2+a^2*y^2*(log(y)^2-1) ,y,x)); */
 424
 425 /*  374  */
 426 /* This equation presents a problem - crashes ode_contrib */
 427 /* (pn_( 374 ),ans:contrib_ode(eqn: ('diff(y,x,1))^2-2*'diff(y,x,1)-y^2 ,y,x)); */
 428
 429 /*  375  */
 430 (pn_(375),ans:contrib_ode(eqn:('diff(y,x,1))^2+a*'diff(y,x,1)+b*x,y,x));
 431 [-((12*b*y+sqrt(a^2-4*b*x)*(4*b*x-a^2)+6*a*b*x)/(12*b))=%c];
 432 [method,ode_check(eqn,ans[1])];
 433 [lie,0];
 434
 435 /*  376  */
 436 (pn_(376),ans:contrib_ode(eqn:('diff(y,x,1))^2+a*'diff(y,x,1)+b*y,y,x));
 437 [[x=%c-((log(%t)*a+2*%t)/b),y=-((%t*a+%t^2)/b)]];
 438 [method,ode_check(eqn,ans[1])];
 439 [lagrange,0];
 440
 441 /*  377  */
 442 (pn_(377),ans:contrib_ode(eqn:('diff(y,x,1))^2+(x-2)*'diff(y,x,1)-y+1,y,x));
 443 [y=%c*x+%c^2-2*%c+1,y=-((x^2-4*x)/4)];
 444 [method,ode_check(eqn,ans[1]),ode_check(eqn,ans[2])];
 445 [clairaut,0,0];
 446
 447 /*  378  */
 448 (pn_(378),ans:contrib_ode(eqn:('diff(y,x,1))^2+(x+a)*'diff(y,x,1)-y,y,x));
 449 [y=%c*x+%c*a+%c^2,y=-((x^2+2*a*x+a^2)/4)];
 450 [method,ode_check(eqn,ans[1]),ode_check(eqn,ans[2])];
 451 [clairaut,0,0];
 452
 453 /*  379  */
 454 (pn_(379),ans:contrib_ode(eqn:('diff(y,x,1))^2-(x+1)*'diff(y,x,1)+y,y,x));
 455 [y=%c*x-%c^2+%c,y=(x^2+2*x+1)/4];
 456 [method,ode_check(eqn,ans[1]),ode_check(eqn,ans[2])];
 457 [clairaut,0,0];
 458
 459 /*  380  */
 460 (pn_(380),ans:contrib_ode(eqn:('diff(y,x,1))^2+2*x*'diff(y,x,1)-y,y,x));
 461 [4*y^3+3*x^2*y^2-18*%c*x*y-12*%c*x^3-9*%c^2=0];
 462 method;
 463 lagrange;
 464
 465 /*  381  */
 466 (pn_(381),ans:contrib_ode(eqn:('diff(y,x,1))^2-2*x*'diff(y,x,1)+y,y,x));
 467 [4*y^3-3*x^2*y^2-18*%c*x*y+12*%c*x^3+9*%c^2=0];
 468 method;
 469 lagrange;
 470
 471 /*  382  */
 472 assume(4*b+a^2>0,c>0);
 473 [4*b+a^2>0,c>0];
 474 (pn_(382),ans:contrib_ode(eqn:('diff(y,x,1))^2+a*x*'diff(y,x,1)-b*x^2-c,y,x));
 475 [-((sqrt(4*b+a^2)*(4*y+a*x^2)+4*c*asinh(sqrt(4*b+a^2)*x/(2*sqrt(c)))+sqrt(4*b+a^2)*x*sqrt((4*b+a^2)*x^2+4*c))/(4*sqrt(4*b+a^2)))=%c];
 476 [method,ode_check(eqn,ans[1])];
 477 [lie,0];
 478 forget(4*b+a^2>0,c>0);
 479 [4*b+a^2>0,c>0];
 480
 481 /*  383  */
 482 /* This equation presents a problem - runs forever */
 483 /* (pn_( 383 ),ans:contrib_ode(eqn: ('diff(y,x,1))^2+a*x*'diff(y,x,1)+b*y+c*x^2 ,y,x)); */
 484
 485 /*  384  */
 486 (pn_(384),ans:contrib_ode(eqn:('diff(y,x,1))^2+(a*x+b)*'diff(y,x,1)-a*y+c,y,x));
 487 [y=(%c*a*x+c+%c*b+%c^2)/a,y=-((a^2*x^2+2*a*b*x-4*c+b^2)/(4*a))];
 488 [method,ode_check(eqn,ans[1]),ode_check(eqn,ans[2])];
 489 [clairaut,0,0];
 490
 491 /*  385  */
 492 /* This equation presents a problem - runs forever */
 493 /* (pn_( 385 ),ans:contrib_ode(eqn: ('diff(y,x,1))^2-2*x^2*'diff(y,x,1)+2*x*y ,y,x)); */
 494
 495 /*  386  */
 496 (pn_(386),ans:contrib_ode(eqn:('diff(y,x,1))^2+a*x^3*'diff(y,x,1)-2*a*x^2*y,y,x));
 497 [-((sqrt(8*a*y+a^2*x^4)+a*x^2)/(sqrt(3)*sqrt(-a)))=%c];
 498 [method,ode_check(eqn,ans[1])];
 499 [lie,0];
 500
 501 /*  387  Not sure about this one - ode_check() chokes
 502          This was "solved" by ode1_lie until Jan 2007. */
 503 (pn_(387),ans:contrib_ode(eqn:('diff(y,x,1))^2+%e^x*('diff(y,x,1)-y),y,x));
 504 false;
 505
 506 /*  388  */
 507 (pn_(388),ans:contrib_ode(eqn:('diff(y,x,1))^2-2*y*'diff(y,x,1)-2*x,y,x));
 508 false;
 509
 510 /*  389  */
 511 (pn_(389),ans:contrib_ode(eqn:('diff(y,x,1))^2-(4*y+1)*'diff(y,x,1)+y*(4*y+1),y,x));
 512 [[x=log(sqrt(8*%t+1)+1)+%c,y=-((sqrt(8*%t+1)-4*%t+1)/8)],[x=log(sqrt(8*%t+1)-1)+%c,y=(sqrt(8*%t+1)+4*%t-1)/8]];
 513 [method,ode_check(eqn,ans[1]),ode_check(eqn,ans[1])];
 514 [lagrange,0,0];
 515
 516 /*  390  */
 517 (pn_(390),ans:contrib_ode(eqn:('diff(y,x,1))^2+a*y*'diff(y,x,1)-b*x-c,y,x));
 518 false;
 519
 520 /*  391  */
 521 (pn_(391),ans:contrib_ode(eqn:('diff(y,x,1))^2+(a*y+b*x)*'diff(y,x,1)+a*b*x*y,y,x));
 522 [y=%c-b*x^2/2,y=%c*%e^-(a*x)];
 523 [method,ode_check(eqn,ans[1]),ode_check(eqn,ans[2])];
 524 [factor,0,0];
 525
 526 /*  392  */
 527 (pn_(392),ans:contrib_ode(eqn:y^2*log(a*y)+('diff(y,x,1))^2-x*y*'diff(y,x,1),y,x));
 528 [x-sqrt(x^2-4*log(a*y))=%c];
 529 [method,ode_check(eqn,ans[1])];
 530 [lie,0];
 531
 532 /*  393  */
 533 /* This equation presents a problem - runs forever */
 534 /* (pn_( 393 ),ans:contrib_ode(eqn: ('diff(y,x,1))^2+2*cot(x)*y*'diff(y,x,1)-y^2 ,y,x)); */
 535
 536 /*  394  */
 537 (pn_(394),ans:contrib_ode(eqn:ode[394],y,x));
 538 false;
 539
 540 /*  395  */
 541 /* This equation presents a problem - runs forever */
 542 /* (pn_( 395 ),ans:contrib_ode(eqn: ('diff(y,x,1))^2+2*f(x)*y*'diff(y,x,1)+g(x)*y^2+h(x) ,y,x)); */
 543
 544 /*  396  */
 545 (pn_(396),ans:contrib_ode(eqn:('diff(y,x,1))^2+y*(y-x)*'diff(y,x,1)-x*y^3,y,x));
 546 [y=%c*%e^(x^2/2),1/y=x+%c];
 547 [method,ode_check(eqn,ans[1]),ode_check(eqn,ans[2])];
 548 [factor,0,0];
 549
 550 /*  397  */
 551 /* This equation presents a problem - runs forever */
 552 /* (pn_( 397 ),ans:contrib_ode(eqn: ('diff(y,x,1))^2-2*x^3*y^2*'diff(y,x,1)-4*x^2*y^3 ,y,x)); */
 553
 554 /*  398  */
 555 /* This equation presents a problem - runs forever */
 556 /* (pn_( 398 ),ans:contrib_ode(eqn: ('diff(y,x,1))^2-3*x*y^(2/3)*'diff(y,x,1)+9*y^(5/3) ,y,x)); */
 557 /*  399  */
 558 (pn_(399),ans:contrib_ode(eqn:2*('diff(y,x,1))^2+(x-1)*'diff(y,x,1)-y,y,x));
 559 [y=%c*x+2*%c^2-%c,y=-((x^2-2*x+1)/8)];
 560 [method,ode_check(eqn,ans[1]),ode_check(eqn,ans[2])];
 561 [clairaut,0,0];
 562
 563 /*  400  */
 564 (pn_(400),ans:contrib_ode(eqn:2*('diff(y,x,1))^2-2*x^2*'diff(y,x,1)+3*x*y,y,x));
 565 [-((2*sqrt(x^4-6*x*y)-2*x^2)/(3*sqrt(x))) = %c];
 566 /* Simplifies to [y=-(3*%c^2*x-4*%c*x^(5/2))/(8*x)] when 3*%c*sqrt(x)-2*x^2 < 0 */
 567 [method,ode_check(eqn,ans[1])];
 568 [lie,0];