share/contrib/diffequations/tests/rtestode_kamke_1_6.mac

   1 (load("contrib_ode"),0);
   2 0$
   3
   4 /* ODE tests - Equations 1.501-1.576
   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 /* Don't kill(all); It messes up trigsimp */
  16
  17 /* Print ode number*/
  18 (pn_(n_):=print("Kamke ODE 1.",n_),true);
  19 true;
  20
  21 /*  501  */
  22 /* This equation presents a problem - runs forever */
  23 /* (pn_( 501 ),ans:contrib_ode(eqn: (a*y^2+b*x+c)*('diff(y,x,1))^2-b*y*'diff(y,x,1)+d*y^2 ,y,x)); */
  24
  25 /*  502  */
  26 /* This equation presents a problem - runs forever */
  27 /* (pn_( 502 ),ans:contrib_ode(eqn: (a*y-b*x)^2*(a^2*('diff(y,x,1))^2+b^2)-c^2*(a*'diff(y,x,1)+b)^2 ,y,x)); */
  28
  29 /*  503  */
  30 /* This equation too general - E S Cheb-Terrab and T Kolokolnikov */
  31 /* (pn_( 503 ),ans:contrib_ode(eqn: (b2*y+a2*x+c2)^2*('diff(y,x,1))^2+(b1*y+a1*x+c1)*'diff(y,x,1)+b0*y+c0+a0 ,y,x)); */
  32
  33 /*  504  */
  34 /* This equation presents a problem - runs forever */
  35 /* (pn_( 504 ),ans:contrib_ode(eqn: x*y^2*('diff(y,x,1))^2-(y^3+x^3-a)*'diff(y,x,1)+x^2*y ,y,x)); */
  36
  37 /*  505  */
  38 (pn_(505),ans:contrib_ode(eqn:x*y^2*('diff(y,x,1))^2-2*y^3*'diff(y,x,1)+2*x*y^2-x^3,y,x));
  39 [y^2/2=x^2/2+%c,-((y^2-x^2)/(2*x^4))=%c];
  40 [method,ode_check(eqn,ans[1]),ode_check(eqn,ans[2])];
  41 [factor,0,0];
  42
  43 /*  506  */
  44 /* This equation presents a problem - runs forever */
  45 /* (pn_( 506 ),ans:contrib_ode(eqn: x^2*(x*y^2-1)*('diff(y,x,1))^2+2*x^2*y^2*(y-x)*'diff(y,x,1)-y^2*(x^2*y-1) ,y,x)); */
  46
  47 /*  507  */
  48 /* This equation presents a problem - runs forever */
  49 /* (pn_( 507 ),ans:contrib_ode(eqn: (y^4-a^2*x^2)*('diff(y,x,1))^2+2*a^2*x*y*'diff(y,x,1)+y^2*(y^2-a^2) ,y,x)); */
  50
  51 /*  508  */
  52 /* This equation presents a problem - runs forever */
  53 /* (pn_( 508 ),ans:contrib_ode(eqn: (y^4+x^2*y^2-x^2)*('diff(y,x,1))^2+2*x*y*'diff(y,x,1)-y^2 ,y,x)); */
  54
  55 /*  509  */
  56 (pn_(509),ans:contrib_ode(eqn:9*(x^2-1)*y^4*('diff(y,x,1))^2-6*x*y^5*'diff(y,x,1)-4*x^2,y,x));
  57 [log(sqrt(y^6+4*x^2-4)+y^3)=%c];
  58 [method,ode_check(eqn,ans[1])];
  59 [lie,0];
  60
  61 /*  510  */
  62 /* This equation presents a problem - runs forever */
  63 /* (pn_( 510 ),ans:contrib_ode(eqn: x^2*(x^2*y^4-1)*('diff(y,x,1))^2+2*x^3*y^3*(y^2-x^2)*'diff(y,x,1)-y^2*(x^4*y^2-1) ,y,x)); */
  64
  65 /*  511  */
  66 /* This equation presents a problem - runs forever */
  67 /* (pn_( 511 ),ans:contrib_ode(eqn: (a^2*sqrt(y^2+x^2)-x^2)*('diff(y,x,1))^2+2*x*y*'diff(y,x,1)+a^2*sqrt(y^2+x^2)-y^2 ,y,x)); */
  68
  69 /*  512  */
  70 /* This equation presents a problem - runs forever */
  71 /* (pn_( 512 ),ans:contrib_ode(eqn: (a*(y^2+x^2)^(3/2)-x^2)*('diff(y,x,1))^2+2*x*y*'diff(y,x,1)+a*(y^2+x^2)^(3/2)-y^2 ,y,x)); */
  72
  73 /*  513  */
  74 /* This equation presents a problem - runs forever */
  75 /* (pn_( 513 ),ans:contrib_ode(eqn: sin(y)*('diff(y,x,1))^2+2*x*cos(y)^3*'diff(y,x,1)-cos(y)^4*sin(y) ,y,x)); */
  76
  77 /*  514  */
  78 (pn_(514),ans:contrib_ode(eqn:(a*cos(y)+b)*('diff(y,x,1))^2-c*cos(y)+d,y,x));
  79 [[x=(-2*a*d-2*b*c)*'integrate(1/(sqrt(c^2-2*%t^2*a*c+%t^4*a^2)*sqrt(-d^2+%t^2*(-2*b*d-2*a*c)+c^2+%t^4*(a^2-b^2))),%t)+%c,y=%pi-acos(d/(%t^2*a-c)+%t^2*b/(%t^2*a-c))]];
  80 [method,ode_check(eqn,ans[1])];
  81 [lagrange,0];
  82
  83 /*  515  */
  84 /* This equation presents a problem - runs forever */
  85 /* (pn_( 515 ),ans:contrib_ode(eqn: (('diff(y,x,1))^2+1)*f(y^2+x^2)-(x*'diff(y,x,1)-y)^2 ,y,x)); */
  86
  87 /*  516  */
  88 /* This equation presents a problem - runs forever */
  89 /* (pn_( 516 ),ans:contrib_ode(eqn: (y^2+x^2)*(('diff(y,x,1))^2+1)*f(x/sqrt(y^2+x^2))-(x*'diff(y,x,1)-y)^2 ,y,x)); */
  90
  91 /*  517  */
  92 /* This equation presents a problem - runs forever */
  93 /* (pn_( 517 ),ans:contrib_ode(eqn: (y^2+x^2)*(('diff(y,x,1))^2+1)*f(y/sqrt(y^2+x^2))-(x*'diff(y,x,1)-y)^2 ,y,x)); */
  94
  95 /*  518  */
  96 (pn_(518),ans:contrib_ode(eqn:('diff(y,x,1))^3-(y-a)^2*(y-b)^2,y,x),0);
  97 0;
  98 /* Expected answer is a mess that changes.  Don't try to track it
  99 [[x=3*('integrate(1/(sqrt(%t)*sqrt(b^2-2*a*b+a^2-4*%t^(3/2))),%t))/2+%c,y=(b+a)/2-sqrt(b^2-2*a*b+a^2-4*%t^(3/2))/2],[x=%c-3*('integrate(1/(sqrt(%t)*sqrt(b^2-2*a*b+a^2-4*%t^(3/2))),%t))/2,y=sqrt(b^2-2*a*b+a^2-4*%t^(3/2))/2+(b+a)/2],[x=%c-3*('integrate(1/(sqrt(%t)*sqrt(b^2-2*a*b+a^2+4*%t^(3/2))),%t))/2,y=(b+a)/2-sqrt(b^2-2*a*b+a^2+4*%t^(3/2))/2],[x=3*('integrate(1/(sqrt(%t)*sqrt(b^2-2*a*b+a^2+4*%t^(3/2))),%t))/2+%c,y=sqrt(b^2-2*a*b+a^2+4*%t^(3/2))/2+(b+a)/2]]; */
 100 [method,ode_check(eqn,ans[1]),ode_check(eqn,ans[2]),ode_check(eqn,ans[3])];
 101 [lagrange,0,0,0];
 102
 103 /*  519  */
 104 /* This equation presents a problem - crashes ode_contrib */
 105 /* (pn_( 519 ),ans:contrib_ode(eqn: ('diff(y,x,1))^3-f(x)*(a*y^2+b*y+c)^2 ,y,x)); */
 106
 107 /*  520  */
 108 (pn_( 520 ),ans:contrib_ode(eqn: ('diff(y,x,1))^3+'diff(y,x,1)-y ,y,x));
 109 [[x = log(%t)+3*%t^2/2+%c,y = %t^3+%t]];
 110 [method,ode_check(eqn,ans[1])];
 111 [lagrange,0];
 112
 113 /*  521  */
 114 (pn_(521),ans:contrib_ode(eqn:('diff(y,x,1))^3+x*'diff(y,x,1)-y,y,x));
 115 [y=%c*x+%c^3,y=-2*sqrt(-x)*x/(3*sqrt(3)),y=2*sqrt(-x)*x/(3*sqrt(3))];
 116 [method,ode_check(eqn,ans[1]),ode_check(eqn,ans[2]),ode_check(eqn,ans[3])];
 117 [clairaut,0,0,0];
 118
 119 /*  522  */
 120 (pn_(522),ans:contrib_ode(eqn:('diff(y,x,1))^3-(x+5)*'diff(y,x,1)+y,y,x));
 121 [y=%c*x-%c^3+5*%c,y=-2*(x+5)^(3/2)/(3*sqrt(3)),y=2*(x+5)^(3/2)/(3*sqrt(3))];
 122 [method,ode_check(eqn,ans[1]),ode_check(eqn,ans[2]),ode_check(eqn,ans[3])];
 123 [clairaut,0,0,0];
 124
 125 /*  523  */
 126 /* This equation presents a problem - crashes ode_contrib */
 127 /* (pn_( 523 ),ans:contrib_ode(eqn: ('diff(y,x,1))^3-a*x*'diff(y,x,1)+x^3 ,y,x)); */
 128
 129 /*  524  */
 130 (pn_(524),ans:contrib_ode(eqn:('diff(y,x,1))^3-2*y*'diff(y,x,1)+y^2,y,x));
 131 [[x=-3*sqrt(1-%t)+2*log(sqrt(1-%t)+1)+%c,y=%t-sqrt(1-%t)*%t],[x=3*sqrt(1-%t)+2*log(sqrt(1-%t)-1)+%c,y=sqrt(1-%t)*%t+%t]];
 132 method;
 133 lagrange;
 134
 135 /*  525  */
 136 /* This equation presents a problem - runs forever */
 137 /* (pn_( 525 ),ans:contrib_ode(eqn: ('diff(y,x,1))^2-a*x*y*'diff(y,x,1)+2*a*y^2 ,y,x)); */
 138
 139 /*  526  */
 140 (pn_(526),ans:contrib_ode(eqn:('diff(y,x,1))^3-(y^2+x*y+x^2)*('diff(y,x,1))^2+(x*y^3+x^2*y^2+x^3*y)*'diff(y,x,1)-x^3*y^3,y,x));
 141 [y=x^3/3+%c,y=%c*%e^(x^2/2),-1/y=x+%c];
 142 [method,ode_check(eqn,ans[1]),ode_check(eqn,ans[2]),ode_check(eqn,ans[3])];
 143 [factor,0,0,0];
 144
 145 /*  527  */
 146 /* This equation presents a problem - crashes ode_contrib */
 147 /* (pn_( 527 ),ans:contrib_ode(eqn: ('diff(y,x,1))^3-x*y^4*'diff(y,x,1)-y^5 ,y,x)); */
 148
 149 /*  528  */
 150 /* This equation presents a problem - crashes ode_contrib */
 151 /* (pn_( 528 ),ans:contrib_ode(eqn: ('diff(y,x,1))^3+a*('diff(y,x,1))^2+b*y+a*b*x ,y,x)); */
 152
 153 /*  529  */
 154 (pn_(529),ans:contrib_ode(eqn:('diff(y,x,1))^3+x*('diff(y,x,1))^2-y ,y,x));
 155 [-8*y^3-(4*x^2-12*x-24*%c-27)*y^2
 156     -(-8*x^3+(-8*%c-12)*x^2-12*%c*x+24*%c^2)*y-4*x^4-(8-8*%c)*x^3
 157     -(4*%c^2-24*%c)*x^2-24*%c^2*x+8*%c^3
 158   = 0];
 159 method;
 160 lagrange;
 161
 162 /*  530  */
 163 (pn_(530),ans:contrib_ode(eqn:('diff(y,x,1))^3-y*('diff(y,x,1))^2+y^2,y,x));
 164 [[x=log(2*sqrt(%t^2-4*%t)+2*%t-4)-sqrt(%t^2-4*%t)+%t+%c,y=-((%t*sqrt(%t^2-4*%t)-%t^2)/2)],[x=-log(2*sqrt(%t^2-4*%t)+2*%t-4)+sqrt(%t^2-4*%t)+%t+%c,y=(%t*sqrt(%t^2-4*%t)+%t^2)/2]];
 165 [method,ode_check(eqn,ans[1]),ode_check(eqn,ans[2])];
 166 [lagrange,0,0];
 167
 168 /*  531  */
 169 (pn_(531),ans:contrib_ode(eqn:('diff(y,x,1))^3-(y^4+x*y^2+x^2)*('diff(y,x,1))^2+(x*y^6+x^2*y^4+x^3*y^2)*'diff(y,x,1)-x^3*y^6,y,x));
 170 [y=x^3/3+%c,-1/y=x^2/2+%c,-1/(3*y^3)=x+%c];
 171 [method,ode_check(eqn,ans[1]),ode_check(eqn,ans[2]),ode_check(eqn,ans[3])];
 172 [factor,0,0,0];
 173
 174 /*  532  */
 175 (pn_(532),ans:contrib_ode(eqn:a*('diff(y,x,1))^3+b*('diff(y,x,1))^2+c*'diff(y,x,1)-y-d,y,x));
 176 [[x=log(%t)*c+(4*%t*b+3*%t^2*a)/2+%c,y=-d+%t*c+%t^2*b+%t^3*a]];
 177 [method,ode_check(eqn,ans[1])];
 178 [lagrange,0];
 179
 180 /*  533  */
 181 (pn_(533),ans:contrib_ode(eqn:x*('diff(y,x,1))^3-y*('diff(y,x,1))^2+a,y,x));
 182 [y=(%c^3*x+a)/%c^2,y=(3*sqrt(3)*%i-3)*a^(1/3)*x^(2/3)/(2*4^(1/3)),y=-((3*sqrt(3)*%i+3)*a^(1/3)*x^(2/3)/(2*4^(1/3))),y=3*a^(1/3)*x^(2/3)/4^(1/3)];
 183 [method,ode_check(eqn,ans[1]),ode_check(eqn,ans[2]),ode_check(eqn,ans[3]),ode_check(eqn,ans[4])];
 184 [clairaut,0,0,0,0];
 185
 186 /*  534  */
 187 (pn_(534),ans:contrib_ode(eqn:4*x*('diff(y,x,1))^3-6*y*('diff(y,x,1))^2+3*y-x,y,x));
 188 [-8*x^2*(9*%c*y^2+6*%c^2*y-2*x^3-6*%c*x^2-6*%c^2*x-%c^3)=0];
 189 method;
 190 lagrange;
 191
 192 /*  535  */
 193 (pn_(535),ans:contrib_ode(eqn:8*x*('diff(y,x,1))^3-12*y*('diff(y,x,1))^2+9*y,y,x));
 194 [-64*x^2*(9*%c*y^2-x^3-9*%c*x^2-27*%c^2*x-27*%c^3)=0];
 195 method;
 196 lagrange;
 197
 198 /*  536  */
 199 (pn_(536),ans:contrib_ode(eqn:(x^2-a^2)*('diff(y,x,1))^3+b*x*(x^2-a^2)*('diff(y,x,1))^2+'diff(y,x,1)+b*x,y,x));
 200 [-((2*y+b*x^2)/2)=%c];
 201 [method,ode_check(eqn,ans[1])];
 202 [lie,0];
 203
 204 /*  537  */
 205 /* This equation presents a problem - crashes ode_contrib */
 206 /* (pn_( 537 ),ans:contrib_ode(eqn: x^3*('diff(y,x,1))^3-3*x^2*y*('diff(y,x,1))^2+(3*x*y^2+x^6)*'diff(y,x,1)-y^3-2*x^5*y ,y,x)); */
 207
 208 /*  538  */
 209 /* This equation presents a problem - crashes ode_contrib */
 210 /* (pn_( 538 ),ans:contrib_ode(eqn: 2*(x*'diff(y,x,1)+y)^3-y*'diff(y,x,1) ,y,x)); */
 211
 212 /*  539  */
 213 (pn_(539),ans:contrib_ode(eqn:sin(x)*('diff(y,x,1))^3-(sin(x)*y-cos(x)^2)*('diff(y,x,1))^2+(-cos(x)^2*y-sin(x))*'diff(y,x,1)+sin(x)*y,y,x));
 214 [[x=log(%t)+%c,y=%t]];
 215 ans[1][2],solve(ans[1][1],%t);
 216 y = %e^(x-%c);
 217 [method,ode_check(eqn,%)];
 218 [lagrange,0];
 219
 220 /*  540  */
 221 (pn_(540),ans:contrib_ode(eqn:2*y*('diff(y,x,1))^3-y*('diff(y,x,1))^2+2*x*'diff(y,x,1)-x,y,x));
 222 [[x=%c*%e^(2*(-log(%t^2-%t+1)/3-log(%t+1)/3+log(%t))),y=-x/%t^2]];
 223 [method,ode_check(eqn,ans[1])];
 224 [lagrange,0];
 225
 226 /*  541  */
 227 /* This equation presents a problem - crashes ode_contrib */
 228 /* (pn_( 541 ),ans:contrib_ode(eqn: y^2*('diff(y,x,1))^3+2*x*'diff(y,x,1)-y ,y,x)); */
 229
 230 /*  542  */
 231 /* This equation presents a problem - crashes ode_contrib */
 232 /* (pn_( 542 ),ans:contrib_ode(eqn: 16*y^2*('diff(y,x,1))^3+2*x*'diff(y,x,1)-y ,y,x)); */
 233
 234 /*  543  */
 235 /* This equation presents a problem - crashes ode_contrib */
 236 /* (pn_( 543 ),ans:contrib_ode(eqn: x*y^2*('diff(y,x,1))^3-y^3*('diff(y,x,1))^2+x*(x^2+1)*'diff(y,x,1)-x^2*y ,y,x)); */
 237
 238 /*  544  */
 239 /* This equation presents a problem - crashes ode_contrib */
 240 /* (pn_( 544 ),ans:contrib_ode(eqn: x^7*y^2*('diff(y,x,1))^3-(3*x^6*y^3-1)*('diff(y,x,1))^2+3*x^5*y^4*'diff(y,x,1)-x^4*y^5 ,y,x)); */
 241
 242 /*  545  */
 243 /* This equation presents a problem - crashes ode_contrib */
 244 /* (pn_( 545 ),ans:contrib_ode(eqn: ('diff(y,x,1))^4-(y-a)^3*(y-b)^2 ,y,x)); */
 245
 246 /*  546  */
 247 /* This equation presents a problem - crashes ode_contrib */
 248 /* (pn_( 546 ),ans:contrib_ode(eqn: ('diff(y,x,1))^4+3*(x-1)*('diff(y,x,1))^2-3*(2*y-1)*'diff(y,x,1)+3*x ,y,x)); */
 249
 250 /*  547  */
 251 /* This equation presents a problem - runs forever */
 252 /* (pn_( 547 ),ans:contrib_ode(eqn: ('diff(y,x,1))^4-4*y*(x*'diff(y,x,1)-2*y)^2 ,y,x)); */
 253
 254 /*  548  */
 255 /* This equation presents a problem - crashes ode_contrib */
 256 /* (pn_( 548 ),ans:contrib_ode(eqn: ('diff(y,x,1))^6-(y-a)^4*(y-b)^3 ,y,x)); */
 257
 258 /*  549  */
 259 (pn_(549),ans:contrib_ode(eqn:x^2*(('diff(y,x,1))^2+1)^3-a^2,y,x));
 260 [(a^(2/3)-x^(2/3))^(3/2)-y=%c];
 261 [method,ode_check(eqn,ans[1])];
 262 [lie,0];
 263
 264 /*  550  */
 265 /* This equation presents a problem - asks question */
 266 /* (pn_( 550 ),ans:contrib_ode(eqn: ('diff(y,x,1))^r-a*y^s-b*x^(r*s/(r-s)) ,y,x)); */
 267
 268 /*  551  */
 269 /* This equation presents a problem - crashes ode_contrib */
 270 /* (pn_( 551 ),ans:contrib_ode(eqn: ('diff(y,x,1))^n-f(x)^n*(y-a)^(n+1)*(y-b)^(n-1) ,y,x)); */
 271
 272 /*  552  */
 273 /* This equation presents a problem - crashes ode_contrib */
 274 /* (pn_( 552 ),ans:contrib_ode(eqn: ('diff(y,x,1))^n-f(x)*g(y) ,y,x)); */
 275
 276 /*  553  */
 277 assume(m>1,n>1);
 278 [m>1,n>1];
 279 (pn_(553),ans:contrib_ode(eqn:b*('diff(y,x,1))^n+a*('diff(y,x,1))^m-y,y,x));
 280 [[x=%t^(n-1)*b*n/(n-1)+%t^(m-1)*a*m/(m-1)+%c,y=%t^n*b+%t^m*a]];
 281 [method,ode_check(eqn,ans[1])];
 282 [lagrange,0];
 283 forget(m>1,n>1);
 284 [m>1,n>1];
 285
 286 /*  554  */
 287 (pn_(554),ans:contrib_ode(eqn:x^(n-1)*('diff(y,x,1))^n-n*x*'diff(y,x,1)+y,y,x));
 288 false;
 289
 290 /*  555  */
 291 (pn_(555),ans:contrib_ode(eqn:sqrt(('diff(y,x,1))^2+1)+x*'diff(y,x,1)-y,y,x));
 292 [y=%c*x+sqrt(%c^2+1),[-y+%t*x+sqrt(%t^2+1)=0,(sqrt(%t^2+1)*x+%t)/sqrt(%t^2+1)=0]];
 293 [method,ode_check(eqn,ans[1]),ode_check(eqn,ans[2])];
 294 [clairaut,0,0];
 295
 296 /*  556  */
 297 (pn_(556),ans:contrib_ode(eqn:sqrt(('diff(y,x,1))^2+1)+x*('diff(y,x,1))^2+y,y,x));
 298 [[x=(-asinh(%t)-sqrt(%t^2+1)+%c)/(%t+1)^2,y=-%t^2*x-sqrt(%t^2+1)]];
 299 [method,ode_check(eqn,ans[1])];
 300 [lagrange,0];
 301
 302 /*  557  */
 303 (pn_(557),ans:contrib_ode(eqn:x*(sqrt(('diff(y,x,1))^2+1)+'diff(y,x,1))-y,y,x));
 304 [[x=%c*%e^(-log(%t^2+1)/2-asinh(%t)),y=(sqrt(%t^2+1)+%t)*x]];
 305 [method,radcan(ode_check(eqn,ans[1]))];
 306 [lagrange,0];
 307
 308 /*  558  */
 309 (pn_(558),ans:contrib_ode(eqn:a*x*sqrt(('diff(y,x,1))^2+1)+x*'diff(y,x,1)-y,y,x));
 310 [[x=%c*%e^(-'integrate(sqrt(%t^2+1)/(%t^2*a+a),%t)-log(%t^2+1)/2),
 311 y=(sqrt(%t^2+1)*a+%t)*x]];
 312 [method,radcan(ode_check(eqn,ans[1]))];
 313 [lagrange,0];
 314
 315 /*  559  */
 316 /* This equation presents a problem - runs forever */
 317 /* (pn_( 559 ),ans:contrib_ode(eqn: y*sqrt(('diff(y,x,1))^2+1)-a*y*'diff(y,x,1)-a*x ,y,x)); */
 318
 319 /*  560  */
 320 (pn_(560),ans:contrib_ode(eqn:a*y*sqrt(('diff(y,x,1))^2+1)-2*x*y*'diff(y,x,1)+y^2-x^2,y,x));
 321 false;
 322
 323 /*  561  */
 324 (pn_(561),ans:contrib_ode(eqn:sqrt(('diff(y,x,1))^2+1)*f(y^2+x^2)-x*'diff(y,x,1)+y,y,x));
 325 false;
 326
 327 /*  562  */
 328 (pn_(562),ans:contrib_ode(eqn:a*(('diff(y,x,1))^3+1)^(1/3)+b*x*'diff(y,x,1)-y,y,x));
 329 [[x=%e^-(log(%t)*b/(b-1))*(%c-a*('integrate(%t*%e^(log(%t)*b/(b-1))/(%t^3+1)^(2/3),%t))/(b-1)),y=%t*b*x+(%t^3+1)^(1/3)*a]];
 330 [method,ode_check(eqn,ans[1])];
 331 [lagrange,0];
 332
 333 /*  563  */
 334 (pn_(563),ans:contrib_ode(eqn:log('diff(y,x,1))+x*'diff(y,x,1)+a*y+b,y,x));
 335 false;
 336
 337 /*  564  Check second solution */
 338 (pn_(564),ans:contrib_ode(eqn:log('diff(y,x,1))+a*(x*'diff(y,x,1)-y),y,x));
 339 [y=(%c*a*x+log(%c))/a,[a*(%t*x-y)+log(%t)=0,(%t*a*x+1)/%t=0]];
 340 [method,ode_check(eqn,ans[1])];
 341 [clairaut,0];
 342
 343 /*  565  */
 344 (pn_(565),ans:contrib_ode(eqn:y*log('diff(y,x,1))+'diff(y,x,1)-y*log(y)-x*y,y,x));
 345 false;
 346
 347 /*  566  */
 348 (pn_(566),ans:contrib_ode(eqn:sin('diff(y,x,1))+'diff(y,x,1)-x,y,x));
 349 false;
 350
 351 /*  567  */
 352 (pn_(567),ans:contrib_ode(eqn:a*cos('diff(y,x,1))+b*'diff(y,x,1)+x,y,x));
 353 false;
 354
 355 /*  568  */
 356 (pn_(568),ans:contrib_ode(eqn:('diff(y,x,1))^2*sin('diff(y,x,1))-y,y,x));
 357 [[x=%t*sin(%t)-cos(%t)+%c,y=%t^2*sin(%t)]];
 358 [method,ode_check(eqn,ans[1])];
 359 [lagrange,0];
 360
 361 /*  569  */
 362 (pn_(569),ans:contrib_ode(eqn:(('diff(y,x,1))^2+1)*sin(x*'diff(y,x,1)-y)^2-1,y,x));
 363 [y=%c*x+asin(1/sqrt(%c^2+1)),[(%t^2+1)*sin(y-%t*x)^2-1=0,2*%t*sin(y-%t*x)^2-(2*%t^2*x+2*x)*cos(y-%t*x)*sin(y-%t*x)=0]];
 364 method;
 365 clairaut;
 366
 367 /*  570  */
 368 (pn_(570),ans:contrib_ode(eqn:(('diff(y,x,1))^2+1)*(arctan('diff(y,x,1))+a*x)+'diff(y,x,1),y,x));
 369 false;
 370
 371 /*  571  */
 372 (pn_(571),ans:contrib_ode(eqn:a*x^n*f('diff(y,x,1))+x*'diff(y,x,1)-y,y,x));
 373 false;
 374
 375 /*  572  */
 376 (pn_(572),ans:contrib_ode(eqn:x*h('diff(y,x,1))+y*g('diff(y,x,1))+(x*'diff(y,x,1)-y)^n*f('diff(y,x,1)),y,x));
 377 false;
 378
 379 /*  573  */
 380 (pn_(573),ans:contrib_ode(eqn:f(x*('diff(y,x,1))^2)+2*x*'diff(y,x,1)-y,y,x));
 381 false;
 382
 383 /*  574  */
 384 (pn_(574),ans:contrib_ode(eqn:f(x-3*('diff(y,x,1))^2/2)+('diff(y,x,1))^3-y,y,x));
 385 false;
 386
 387 /*  575  */
 388 (pn_(575),ans:contrib_ode(eqn:'diff(y,x,1)*f(x*y*'diff(y,x,1)-y^2)-x^2*'diff(y,x,1)+x*y,y,x));
 389 false;
 390
 391 /*  576  */
 392 /* This equation too general - E S Cheb-Terrab and T Kolokolnikov */
 393 /* (pn_( 576 ),ans:contrib_ode(eqn: phi(f(x,y,'diff(y,x,1)),g(x,y,'diff(y,x,1))) ,y,x)); */
 394