rtest_odesolve_1_4.mac

/* ODE tests - Equations 1.301-1.400

  Reference:
    E Kamke, Differentialgleichungen Losungsmethoden und Losungen, 
    Vol 1, Geest & Portig, Leipzig, 1961

    E. S. Cheb-Terrab, T. Koloknikov,  First Order ODEs, 
    Symmetries and Linear Transformations, European Journal of 
    Applied Mathematics, Vol. 14, No. 2, pp. 231-246 (2003). 
    (http://lie.uwaterloo.ca/papers/ode_iv.pdf)

*/
/* Don't kill(all); It messes up trigsimp */

/* Print ode number*/
(kill (all),
batch("~/mathematics/maxima_files/ode1_lie.mac"), 
batch("~/mathematics/maxima_files/kamke1_1.mac"), 
DEBUGFLAG:2,
timer:[],
/* Print ode number*/
pn_(n_):=(print("Kamke ODE 1.",n_),t0:elapsed_run_time()),
pt_(n_):=(t:elapsed_run_time()-t0,print("time for ODE 1.",n_,"= ",t),timer:endcons([n_,t],timer)),

/*  301  */ 
pn_(301),ans:ode1solve(eqn:kamke1[301],y,x),pt_(301),ans);
[(x*log(x*y)+3*y^2)/x = %c];

/*  302  */ 
(pn_(302),ans:ode1solve(eqn:kamke1[302],y,x,'returnExplicit=false),pt_(302),ans);
[(x*y^2-1)/(x*y) = %c];

/*  303  */ 
(pn_(303),ans:ode1solve(eqn:kamke1[303],y,x),pt_(303),ans);
[(2*x*y*log(y)-x^2*y^2+1)/(x*y) = %c];

/*  304  */ 
(pn_(304),ans:ode1solve(eqn:kamke1[304],y,x,'returnExplicit=false),pt_(304),ans);
[sqrt(10)*log(y^2*(5*x^2*y^2+2))+2*atan((sqrt(5)*x*y)/sqrt(2)) = %c];
/*[sqrt(2)*sqrt(5)*log(y^2*(5*x^2*y^2+2))+2*atan((sqrt(5)*x*y)/sqrt(2)) = %c];*/

/*  305  */ 
(pn_(305),ans:ode1solve(eqn:kamke1[305],y,x,'returnExplicit=false),pt_(305),ans);
[3*y^4-36*x*y+4*x^3 = %c];

/*  306  */ 
(pn_(306),ans:ode1solve(eqn:kamke1[306],y,x,'returnExplicit=false),pt_(306),ans);
[y^3*(y^3-2*x^3) = %c];

/*  307  */ 
(pn_(307),ans:ode1solve(eqn:kamke1[307],y,x,'returnExplicit=false),pt_(307),ans);
[y^4+(2*x^2+2*a)*y^2+x^4-2*a*x^2 = %c];

/*  308  */ 
(pn_(308),ans:ode1solve(eqn:kamke1[308],y,x,'returnExplicit=false),pt_(308),ans);
[2*y^2+x^2 = %c];

/*  309  */ 
(pn_(309),ans:ode1solve(eqn:kamke1[309],y,x,'returnExplicit=false),pt_(309),ans);
[(y-x)*(y+x)*(y^2+x^2+1) = %c];

/*  310  */ 
(pn_(310),ans:ode1solve(eqn:kamke1[310],y,x,'returnExplicit=false),pt_(310),ans);
[2*y^4+10*x^2*y^2+x^4 = %c];

/*  311  */ 
(pn_(311),ans:ode1solve(eqn:kamke1[311],y,x,'returnExplicit=false),pt_(311),ans);
[5*y^4-x*y^3+3*x^2*y^2+3*x^3*y+x^4=%c];

/*  312  */ 
(pn_( 312 ),ans:ode1solve(eqn: kamke1[312] ,y,x),pt_(312),ans); 
[2*a*b*log(a*y^2+b*x^2-a*b)+(b+a)*y^2+(b+a)*x^2 = %c]; 

/*  313  */ 
(pn_( 313 ),ans:ode1solve(eqn:kamke1[313] ,y,x,'returnExplicit=false),pt_(313),ans); 
[(y+x)/(2*a*y^3+(2*c*x+c)*y+2*b*x^3+c*x) = %c];
/*[(a*y^3+c*x*y+b*x^3)/(y+x) = %c]; */

/*  314  */ 
(pn_(314),ans:ode1solve(eqn:kamke1[314],y,x,'returnExplicit=false),pt_(314),ans);
[x^4*y^4+(96*x-16*x^3)*sin(x)+(4*x^4-48*x^2+96)*cos(x) = %c];

/*  315  */ 
(pn_(315),ans:ode1solve(eqn:kamke1[315],y,x,'returnExplicit=false),pt_(315),ans);
[(x*y)/((y+x)*(y^2-x*y+x^2)) = %c];

/*  316  */ 
/* mu= exp(y^2/2)/2*/
(pn_(316),ans:ode1solve(eqn:kamke1[316],y,x),pt_(316),ans);
[(2*x*y^2-4*x+1)*%e^(y^2/2) = %c];
/*[(2*x*y^2-4*x+1)*%e^(y^2/2) = %c];*/
/*[4*x*%e^(y^2/2)-gamma_incomplete(0,-y^2/2) = %c];*/

/*  317  */ 
/* symmetries [0,y^2/(2*y^3+y+x)], symmetry 5 with degree 3, need to increase SYM5DEGREE */
(pn_( 317 ),
SYM5DEGREE:3,
ans:ode1solve(eqn: kamke1[317] ,y,x),
SYM5DEGREE:2,
pt_(317),ans);  
[(y*log(x*y)+y^3-x)/y = %c];

/*  318  */ 
(pn_(318),ans:ode1solve(eqn:kamke1[318],y,x),pt_(318),ans);
[sqrt(y^2-2)*(x*y^2+1) = %c];

/*  319  */ 
(pn_(319),ans:ode1solve(eqn:kamke1[319],y,x),pt_(319),ans);
[y*(10*x*y^6+2*y^4-100*x*y^3-25*y+250*x) = %c];

/*  320  */ 
(pn_(320),ans:ode1solve(eqn:kamke1[320],y,x),pt_(320),ans);
[((x*y^2-2*x+1)*%e^(y^2/2))/x = %c];

/*  321  */ 
(pn_( 321 ),ans:ode1solve(eqn: kamke1[321] ,y,x),pt_(321),ans); 
[((2*x*y+x)*log(2*y+1)+4*x*y^3-2*x*y^2-2*x*y+8)/(x*(2*y+1)) = %c]; 

/*  322  */
(pn_(322),ans:ode1solve(eqn:kamke1[322],y,x,'returnExplicit=false),pt_(322),ans);
[5*x^2*y^4-2*y^3-4*y+x^2 = %c];

/*  323  */ 
(pn_( 323 ),ans:ode1solve(eqn:kamke1[323] ,y,x,'returnExplicit=false),pt_(323),ans); 
[(x*y)/(a*x*y^3+(b*x^3+a*x)*y-2*c) = %c]; 

/*  324  */ 
(pn_( 324 ),ans:ode1solve(eqn: kamke1[324] ,y,x,'returnExplicit=false),pt_(324),ans); 
[(4*x^2*y^3+4*x^3*y^2+1)/(x^2*y^2) = %c]; 

/*  325  */ 
(pn_(325),ans:ode1solve(eqn:kamke1[325],y,x),pt_(325),ans);
['integrate((8*y^3+9*x*y^2+12*x^2*y-x^3)/(y^4+x*y^3+3*x^2*y^2+x^3*y+x^4),y)-log(y-x)=%c];
/*[%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)];*/

/*  326  */ 
/* the solution hangs when trying to solve explicitly*/
(pn_(326),ans:ode1solve(eqn:kamke1[326],y,x,'returnExplicit=false),pt_(326),ans);
[(a*y+b*x)^2/(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) = %c];
/*[%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)];*/

/*  327  */ 
/* inverse-riccati */
/* nijso: sometimes we get the trig solution, sometimes the algebraic one*/
(pn_( 327 ),
ans:ode1solve(eqn: kamke1[327] ,y,x,'tryInverse=true,'returnExplicit=false),
pt_(327),ans); 
/*[(x*y^3-1)/(y*(y+x)) = %c];*/
[atan(y^2)+atan(x*y) = %c]; 

/*  328  */ 
(pn_(328),
assume(not equal(n+1,-1)),
ans:ode1solve(eqn:kamke1[328],y,x),
forget(not equal(n+1,-1)),
pt_(328),ans);
[(y^2*(a*x*y^n-n-2))/x = %c];
/*[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))];*/

/*  329  */ 
(pn_(329),ans:ode1solve(eqn:kamke1[329],y,x),pt_(329),ans);
[Beta*a*log((a*n-b*m)/((a*n-b*m)*x^n*y^m+Alpha*n-Beta*m))+Alpha*b*log(((a*n-b*m)*x^n*y^m+Alpha*n-Beta*m)/(a*n-b*m))+(Alpha*a*n-Alpha*b*m)*log(y)+(Beta*a*n-Beta*b*m)*log(x) = %c];
/*[a*beta*log((a*n-b*m)/((a*n-b*m)*x^n*y^m+alpha*n-beta*m))
  +alpha*b*log(((a*n-b*m)*x^n*y^m+alpha*n-beta*m)/(a*n-b*m))
  +(a*alpha*n-alpha*b*m)*log(y)+(a*beta*n-b*beta*m)*log(x)
   = %c];*/
/*[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))];*/

/*  330  */
/* nijso: check solution!*/ 
(pn_(330),ans:ode1solve(eqn: kamke1[330] ,y,x),pt_(330),ans); 
['integrate('integrate(pderivop(f,1)(y+x),y)-f(y+x),x)-'integrate(f(y+x),y)-y = %c];
/*[y = (f(%g1)*x+%c)/('diff(f(%g1),%g1,1)*x-f(%g1)-1)];*/

/*  331  */ 
/* This equation too general - E S Cheb-Terrab and T Kolokolnikov */ 
/* (pn_( 331 ),ans:ode1solve(eqn: ode[331] ,y,x),pt_(331),ans); */ 
(pn_(331),
ans:false,
pt_(331),ans);
false;

/*  332  */ 
(pn_(332),
ans:ode1solve(eqn:kamke1[332],y,x),pt_(332),ans);
[sqrt(1/(x*y))*(log(x/y)*sqrt(x*y)-2) = %c];
/*[(sqrt(x)*log(x/y)*sqrt(y)-2)/(sqrt(x)*sqrt(y)) = %c];*/
/*[(sqrt(x)*sqrt(y)*(log(y)-log(x))+2)/(sqrt(x)*sqrt(y)) = %c];*/
/*[x=%c*%e^((sqrt(x*y)*log(x*y)+2)/(2*sqrt(x*y)))];*/

/*  333  */ 
(pn_(333),ans:ode1solve(eqn: kamke1[333],y,x),
pt_(333),ans);  
[sqrt(1/(x^3*y^3))*(3*log(x/y^2)*sqrt(x^3*y^3)+6*sqrt(x^2)*y-2) = %c];
/*[(3*x^(3/2)*log(x/y^2)*y^(3/2)+6*abs(x)*y-2)/(x^(3/2)*y^(3/2)) = %c];*/
/*[(sqrt(x)*sqrt(y)*(6*x*y*log(y)-3*x*log(x)*y)-6*abs(x)*y+2)/(x^(3/2)*y^(3/2)) = %c];*/

/*  334  */ 
(pn_(334),ans:ode1solve(eqn: kamke1[334] ,y,x),pt_(334),ans); 
[2*sqrt(y+x)+y = %c]; 

/*  335  */ 
(pn_(335),ans:ode1solve(eqn:kamke1[335],y,x),pt_(335),ans);
[log((sqrt((x-1)*(x+1))+x)/(sqrt((y-1)*(y+1))+y))+y*sqrt((y-1)*(y+1))-x*sqrt((x-1)*(x+1)) = %c];
/*[log((sqrt(x-1)*sqrt(x+1)+x)/(sqrt(y-1)*sqrt(y+1)+y))
  +sqrt(y-1)*y*sqrt(y+1)-sqrt(x-1)*x*sqrt(x+1)
   = %c];*/
/*[log(sqrt(y-1)*sqrt(y+1)+y)-sqrt(y-1)*y*sqrt(y+1)-log(sqrt(x-1)*sqrt(x+1)+x)+sqrt(x-1)*x*sqrt(x+1) = %c];*/
/*[(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];*/

/*  336  */ 
(pn_(336),ans:ode1solve(eqn:kamke1[336],y,x),pt_(336),ans);
[log((sqrt(x^2+1)+x)*(sqrt(y^2+1)+y))+y*sqrt(y^2+1)+2*a*x*y+x*sqrt(x^2+1)
   = %c];
/*[log(sqrt(y^2+1)+y)+y*sqrt(y^2+1)+2*a*x*y+log(sqrt(x^2+1)+x)+x*sqrt(x^2+1) = %c];*/
/*[(asinh(y)+y*sqrt(y^2+1)+2*a*x*y+asinh(x)+x*sqrt(x^2+1))/2=%c];*/

/*  337  */ 
(pn_(337),
assume(%c>0,x>0),
ans:ode1solve(eqn: kamke1[337] ,y,x,'returnExplicit=false),pt_(337),
forget(%c>0,x>0),
ans);  
[1/(sqrt(y^2+x^2)-x) = %c];

/*  338  */
(pn_(338),
ans:ode1solve(eqn: kamke1[338] ,y,x),
pt_(338),ans); 
[(4*(y^2+x^2)^4)/((sin(Alpha)^4+6*sin(Alpha)^2+1)*y^4
                 +sqrt(y^2+x^2)*((4*sin(Alpha)^3+4*sin(Alpha))*y^3
                                +((-12*cos(Alpha)*sin(Alpha)^2)-4*cos(Alpha))
                                 *x*y^2+(12*cos(Alpha)^2+4)*sin(Alpha)*x^2*y
                                +((-4*cos(Alpha)^3)-4*cos(Alpha))*x^3)
                 +((-4*cos(Alpha)*sin(Alpha)^3)-12*cos(Alpha)*sin(Alpha))
                  *x*y^3
                 +((6*cos(Alpha)^2+6)*sin(Alpha)^2+6*cos(Alpha)^2+2)*x^2*y^2
                 +((-4*cos(Alpha)^3)-12*cos(Alpha))*sin(Alpha)*x^3*y
                 +(cos(Alpha)^4+6*cos(Alpha)^2+1)*x^4)
   = %c];


/*  339  */ 
(pn_( 339 ),ans:ode1solve(eqn: kamke1[339] ,y,x),pt_(339),ans); 
[sqrt(y^2+x^2+1)+atan(x/y) = %c]; 

/*  340 */ 
/* takes too long... */
(pn_(340),
ans:true,
/*ode1solve(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),*/
pt_(340),ans);
false;
/*
[-'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];
*/
/*  341  */ 
(pn_(341),ans:ode1solve(eqn:kamke1[341],y,x),
pt_(341),ans);
[x*%e^y+%e^x*y=%c];

/*  342  */ 
(pn_(342),ans:ode1solve(eqn:kamke1[342],y,x,'returnExplicit=false),
pt_(342),ans);
[%e^-(x*y)*(3*%e^(2*x*y)+log(x)*%e^(x*y)-2)=%c];

/*  343  */ 
(pn_(343),ans:ode1solve(eqn:kamke1[343],y,x),pt_(343),ans);
[%e^-y*(log(y)+gamma_incomplete(0,y)*%e^y+x) = %c];

/*  344  */ 
(pn_(344),ans:ode1solve(eqn:kamke1[344],y,x),pt_(344),ans);
[(log(y)+2*x)/y = %c];

/*  345  */ 
(pn_(345),ans:ode1solve(eqn:kamke1[345],y,x),pt_(345),ans);
[(y*(2*x^2*y*log(y)-x^2*y+2))/x^2 = %c];

/*  346  */ 
(pn_( 346 ),ans:ode1solve(eqn: kamke1[346] ,y,x),pt_(346),ans); 
[(y-a*x)*log(x*y) = %c]; 

/*  347  */ 
(pn_(347),ans:ode1solve(eqn:kamke1[347],y,x),pt_(347),ans);
[y = acos(2*%c*sin(x)+2*%c+1)];

/*  348  */ 
(pn_(348),ans:ode1solve(eqn:kamke1[348],y,x),pt_(348),ans);
[x*sin(y)+sin(x)*y=%c];

/*  349  */ 
/* we get an implicit solution now... */
(pn_(349),ans:ode1solve(eqn:kamke1[349],y,x),
pt_(349),ans);
/*[%c*x=%e^(1/(2*sin(y/x)))];*/
/*solve(map(log,ans[1]),y);*/
[csc(y/x)*(2*log(x)*sin(y/x)-1) = %c];
/*[y=x*asin(1/(2*log(%c*x)))];*/

/*  350  */
/* separability check failed */
(pn_(350),
ans:false,
ans:ode1solve(eqn:kamke1[350],y,x,'tryInverse=true),
pt_(350),
ans);
[%e^x*sqrt(cos(y)^2)*csc(2*y)*(sin(y+x)-cos(y+x)+sin(y-x)+cos(y-x)+4) = %c];
/*[2/sin(y)+cos(x)+sin(x)=%c*exp(-x)]; */

/*  351  */ 
/* */
(pn_( 351 ),
ans:ode1solve(eqn: kamke1[351] ,y,x,'tryInverse=true),
pt_(351),
ans); 
[%e^-x^2*csc(y)^2*(sqrt(%pi)*(%e^x^2*erf(x)*cos(2*y)-%e^x^2*erf(x))-cos(2*y)-1) = %c];
/*[cot(y)^2=exp(x^2)*(%c-2*'integrate(exp(-x^2),x))];*/

/*  352  */ 
(pn_(352),ans:ode1solve(eqn:kamke1[352],y,x),pt_(352),ans);
[sin(y + x + Alpha) - sin(y + x - Alpha) - sin(y - x + Alpha) + sin(y - x - Alpha) + sin(2*y) + 2*y + sin(2*x) + 2*x = %c];
/*[sin(2*y)-4*sin(alpha)*sin(x)*sin(y)+2*y+sin(2*x)+2*x = %c];*/

/*  353  */ 
/* nijso: minus sign can be absorbed*/
(pn_(353),ans:ode1solve(eqn:kamke1[353],y,x),pt_(353),ans);
[y = -asin(%c/x)];

/*  354  */ 
(pn_(354),ans:ode1solve(eqn:kamke1[354],y,x),pt_(354),ans);
[sec(y)*(sin(y)-x) = %c];

/*  355  */ 
(pn_(355),ans:ode1solve(eqn:kamke1[355],y,x),pt_(355),ans);
[x*sin(y)+cos(x)*y=%c];

/*  356  */ 
(pn_(356),ans:ode1solve(eqn:kamke1[356],y,x),pt_(356),ans);
[x^2*sin(y)+sin(x)*y^2=%c];

/*  357  */ 
(pn_(357),
ans:ode1solve(eqn:kamke1[357],y,x,'tryInverse=true),
pt_(357),
ans);
[y=acos(log(x)/(x+%c))];
/*[(x*%c)*cos(y)=log(x)];*/

/*  358  */ 
(pn_(358),ans:ode1solve(eqn:kamke1[358],y,x),pt_(358),ans);
[y = acos(%c*sec(x))];

/*  359  */ 
(pn_(359),ans:ode1solve(eqn:kamke1[359],y,x,'returnExplicit=false),pt_(359),ans);
[3*tan(y)^2+10*log(sin(x)) = %c];

/*  360  */ 
(pn_(360),
ans:ode1solve(eqn:kamke1[360],y,x,'returnExplicit=false),
pt_(360),
ans);
['integrate(cos(a*y)/((c*cos(a*y)-1)*sqrt(cos(a*y)^2+c*cos(a*y)-1)),y)+b*x
   = %c];

/*  361  */ 
(pn_(361),ans:ode1solve(eqn:kamke1[361],y,x),pt_(361),ans);
[sin(y+x)-cos(x*y)+cos(y)+sin(x)=%c];

/*  362  */ 
(pn_(362),ans:ode1solve(eqn:kamke1[362],y,x),pt_(362),ans);
[log(x*y^4)+cos(x*y) = %c];

/*  363  */ 
(pn_(363),ans:ode1solve(eqn:kamke1[363],y,x),pt_(363),ans);
[(x*sin((2*y)/x)+2*y+4*x*log(x))/x = %c];

/*  364  */ 
(pn_(364),ans:ode1solve(eqn:kamke1[364],y,x),pt_(364),ans);
[2*x^2*y^2*(cos((2*y)/x)+1) = %c];

/*  365  */ 
/* nijso: check result!*/
(pn_( 365 ),ans:ode1solve(eqn: kamke1[365] ,y,x),pt_(365),ans); 
['integrate((x*((2*y^2+2*x^2)*'integrate((y*((y^2+x^2)*pderivop(f,1)(y^2+x^2)-f(y^2+x^2)))/(y^2+x^2)^2,y)-f(y^2+x^2)))/(y^2+x^2),x)-'integrate((y*f(y^2+x^2))/(y^2+x^2),y)+atan(y/x) = %c];
/*[('diff(f(%g1),%g1,1)*y^2+'diff(f(%g1),%g1,1)*x^2-f(%g1))*log(y^2+x^2)
  -'diff(f(%g1),%g1,1)*y^2-2*atan(x/y)-'diff(f(%g1),%g1,1)*x^2
   = %c]; 
*/

/*  366  */ 
/* nijso: check result */
(pn_(366),ans:ode1solve(eqn:kamke1[366],y,x,'returnExplicit=false),pt_(366),ans);
['integrate(x*(2*a*'integrate(y*pderivop(f,1)(a*y^2+x^2),y)-f(a*y^2+x^2)),x)-a*'integrate(y*f(a*y^2+x^2),y)+x*y = %c];
/*[y = (x-sqrt(((%g1*f(%g1)*'diff(f(%g1),%g1,1)-f(%g1)^2)*a+1)*x^2
              -2*%c*f(%g1)*a))
   /(f(%g1)*a),
 y = (sqrt(((%g1*f(%g1)*'diff(f(%g1),%g1,1)-f(%g1)^2)*a+1)*x^2-2*%c*f(%g1)*a)
   +x)
   /(f(%g1)*a)];
*/
/*['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];*/

/*  367  */ 
(pn_( 367 ),ans:ode1solve(eqn: kamke1[367] ,y,x),pt_(367),ans); 
true; 

/* ************************************************************** */

/*  368  */ 
/*
(pn_( 368 ),ans:ode1solve(eqn: ('diff(y,x,1))^2+a*y+b*x^2 ,y,x),pt_(368),ans); 
true; 
*/

/*  369  */
/*
(pn_(369),
assume(a>0),
ans:ode1solve(eqn:('diff(y,x,1))^2+y^2-a^2,y,x),
forget(a>0),
pt_(369),
ans
);
[[x=asin(%t/abs(a))+%c,y=-sqrt(a^2-%t^2)],[x=%c-asin(%t/abs(a)),y=sqrt(a^2-%t^2)]];
*/
/*  370  */ 
/* This equation too general - E S Cheb-Terrab and T Kolokolnikov */ 
/*
(pn_( 370 ),ans:ode1solve(eqn: ('diff(y,x,1))^2+y^2-f(x)^2 ,y,x),pt_(370),ans);  
false;
*/
/*  371  */ 
/*
(pn_( 371 ),ans:ode1solve(eqn: ('diff(y,x,1))^2-y^3+y^2 ,y,x),pt_(371),ans);  
true;
*/
/*  372  */ 
/*
(pn_( 372 ),ans:ode1solve(eqn: ('diff(y,x,1))^2-4*y^3+a*y+b ,y,x),pt_(372),ans); 
true; 
*/
/*  373  */ 
/*(pn_( 373 ),ans:ode1solve(eqn: ('diff(y,x,1))^2+a^2*y^2*(log(y)^2-1) ,y,x),pt_(373),ans); 
true; 
*/
/*  374  */ 
/*
(pn_( 374 ),ans:ode1solve(eqn: ('diff(y,x,1))^2-2*'diff(y,x,1)-y^2 ,y,x),pt_(374),ans); 
true; 
*/
/*  375  */ 
/*(pn_(375),ans:ode1solve(eqn:('diff(y,x,1))^2+a*'diff(y,x,1)+b*x,y,x),pt_(375),ans);
[-((12*b*y+sqrt(a^2-4*b*x)*(4*b*x-a^2)+6*a*b*x)/(12*b))=%c];
*/
/*  376  */ 
/*
(pn_(376),ans:ode1solve(eqn:('diff(y,x,1))^2+a*'diff(y,x,1)+b*y,y,x),pt_(376),ans);
[[x=%c-((log(%t)*a+2*%t)/b),y=-((%t*a+%t^2)/b)]];
*/
/*  377  */ 
/*(pn_(377),ans:ode1solve(eqn:('diff(y,x,1))^2+(x-2)*'diff(y,x,1)-y+1,y,x),pt_(377),ans);
[y=%c*x+%c^2-2*%c+1,y=-((x^2-4*x)/4)];
*/
/*  378  */ 
/*(pn_(378),ans:ode1solve(eqn:('diff(y,x,1))^2+(x+a)*'diff(y,x,1)-y,y,x),pt_(378),ans);
[y=%c*x+%c*a+%c^2,y=-((x^2+2*a*x+a^2)/4)];
*/
/*  379  */ 
/*(pn_(379),ans:ode1solve(eqn:('diff(y,x,1))^2-(x+1)*'diff(y,x,1)+y,y,x),pt_(379),ans);
[y=%c*x-%c^2+%c,y=(x^2+2*x+1)/4];
*/
/*  380  */ 
/*(pn_(380),ans:ode1solve(eqn:('diff(y,x,1))^2+2*x*'diff(y,x,1)-y,y,x),pt_(380),ans);
[4*y^3+3*x^2*y^2-18*%c*x*y-12*%c*x^3-9*%c^2=0];
*/
/*  381  */ 
/*(pn_(381),ans:ode1solve(eqn:('diff(y,x,1))^2-2*x*'diff(y,x,1)+y,y,x),pt_(381),ans);
[4*y^3-3*x^2*y^2-18*%c*x*y+12*%c*x^3+9*%c^2=0];
*/
/*  382  */ 
/*(pn_(382),
assume(4*b+a^2>0,c>0),
ans:ode1solve(eqn:('diff(y,x,1))^2+a*x*'diff(y,x,1)-b*x^2-c,y,x),
forget(4*b+a^2>0,c>0),
pt_(382),
ans
);
[-((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];
*/

/*  383  */ 
/*
(pn_( 383 ),ans:ode1solve(eqn: ('diff(y,x,1))^2+a*x*'diff(y,x,1)+b*y+c*x^2 ,y,x),pt_(383),ans);  
true;
*/

/*  384  */ 
/*
(pn_(384),ans:ode1solve(eqn:('diff(y,x,1))^2+(a*x+b)*'diff(y,x,1)-a*y+c,y,x),pt_(384),ans);
[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))];
*/

/*  385  */ 
/*
(pn_( 385 ),ans:ode1solve(eqn: ('diff(y,x,1))^2-2*x^2*'diff(y,x,1)+2*x*y ,y,x),pt_(385),ans); 
true; 
*/

/*  386  */ 
/*
(pn_(386),ans:ode1solve(eqn:('diff(y,x,1))^2+a*x^3*'diff(y,x,1)-2*a*x^2*y,y,x),pt_(386),ans);
[-((sqrt(8*a*y+a^2*x^4)+a*x^2)/(sqrt(3)*sqrt(-a)))=%c];
*/

/*  387  Not sure about this one - ode_check() chokes
         This was "solved" by ode1_lie until Jan 2007. */
/*
(pn_(387),ans:ode1solve(eqn:('diff(y,x,1))^2+%e^x*('diff(y,x,1)-y),y,x),pt_(387),ans);
false;
*/

/*  388  */ 
/*
(pn_(388),ans:ode1solve(eqn:('diff(y,x,1))^2-2*y*'diff(y,x,1)-2*x,y,x),pt_(388),ans);
false;
*/
/*  389  */ 
/*
(pn_(389),ans:ode1solve(eqn:('diff(y,x,1))^2-(4*y+1)*'diff(y,x,1)+y*(4*y+1),y,x),pt_(389),ans);
[[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]];
*/

/*  390  */ 
/*
(pn_(390),ans:ode1solve(eqn:('diff(y,x,1))^2+a*y*'diff(y,x,1)-b*x-c,y,x),pt_(390),ans);
false;
*/

/*  391  */ 
/*
(pn_(391),ans:ode1solve(eqn:('diff(y,x,1))^2+(a*y+b*x)*'diff(y,x,1)+a*b*x*y,y,x),pt_(391),ans);
[y=%c-b*x^2/2,y=%c*%e^-(a*x)];
*/

/*  392  */ 
/*
(pn_(392),ans:ode1solve(eqn:y^2*log(a*y)+('diff(y,x,1))^2-x*y*'diff(y,x,1),y,x),pt_(392),ans);
[x-sqrt(x^2-4*log(a*y))=%c];
*/

/*  393  */ 
/*
(pn_( 393 ),ans:ode1solve(eqn: ('diff(y,x,1))^2+2*cot(x)*y*'diff(y,x,1)-y^2 ,y,x),pt_(393),ans); 
true; 
*/

/*  394  */ 
/*
(pn_(394),ans:ode1solve(eqn:ode[394],y,x),pt_(394),ans);
false;
*/

/*  395  */ 
/*
(pn_( 395 ),ans:ode1solve(eqn: ('diff(y,x,1))^2+2*f(x)*y*'diff(y,x,1)+g(x)*y^2+h(x) ,y,x),pt_(395),ans);  
true;
*/

/*  396  */ 
/*
(pn_(396),ans:ode1solve(eqn:('diff(y,x,1))^2+y*(y-x)*'diff(y,x,1)-x*y^3,y,x),pt_(396),ans);
[y=%c*%e^(x^2/2),1/y=x+%c];
*/

/*  397  */ 
/*
(pn_( 397 ),ans:ode1solve(eqn: ('diff(y,x,1))^2-2*x^3*y^2*'diff(y,x,1)-4*x^2*y^3 ,y,x),pt_(397),ans);  
true;
*/

/*  398  */ 
/*
(pn_( 398 ),ans:ode1solve(eqn: ('diff(y,x,1))^2-3*x*y^(2/3)*'diff(y,x,1)+9*y^(5/3) ,y,x),pt_(398),ans); 
true;
*/
 
/*  399  */ 
/*
(pn_(399),ans:ode1solve(eqn:2*('diff(y,x,1))^2+(x-1)*'diff(y,x,1)-y,y,x),pt_(399),ans);
[y=%c*x+2*%c^2-%c,y=-((x^2-2*x+1)/8)];
*/

/*  400  */ 
/*
(pn_(400),ans:ode1solve(eqn:2*('diff(y,x,1))^2-2*x^2*'diff(y,x,1)+3*x*y,y,x),pt_(400),ans);
[-((2*sqrt(x^4-6*x*y)-2*x^2)/(3*sqrt(x))) = %c];
*/
/* Simplifies to [y=-(3*%c^2*x-4*%c*x^(5/2))/(8*x)] when 3*%c*sqrt(x)-2*x^2 < 0 */


(print("timings: ",timer,", total=",lsum(i,i,makelist(timer[i][2],i,1,length(timer)))),true);
true;