60.2.312 problem 890

Internal problem ID [10886]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 890
Date solved : Sunday, March 30, 2025 at 07:20:07 PM
CAS classification : [_rational]

\begin{align*} y^{\prime }&=\frac {x}{-y+1+y^{4}+2 x^{2} y^{2}+x^{4}+y^{6}+3 x^{2} y^{4}+3 x^{4} y^{2}+x^{6}} \end{align*}

✓ Maple. Time used: 0.137 (sec). Leaf size: 496

ode:=diff(y(x),x) = x/(-y(x)+1+y(x)^4+2*x^2*y(x)^2+x^4+y(x)^6+3*x^2*y(x)^4+3*x^4*y(x)^2+x^6); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 0.213 (sec). Leaf size: 228

ode=D[y[x],x] == x/(1 + x^4 + x^6 - y[x] + 2*x^2*y[x]^2 + 3*x^4*y[x]^2 + y[x]^4 + 3*x^2*y[x]^4 + y[x]^6); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{y(x)}\left (-\frac {K[2]}{x^6+3 K[2]^2 x^4+x^4+3 K[2]^4 x^2+2 K[2]^2 x^2+K[2]^6+K[2]^4+1}-\int _1^x\frac {K[1] \left (6 K[2]^5+12 K[1]^2 K[2]^3+4 K[2]^3+6 K[1]^4 K[2]+4 K[1]^2 K[2]\right )}{\left (K[1]^6+3 K[2]^2 K[1]^4+K[1]^4+3 K[2]^4 K[1]^2+2 K[2]^2 K[1]^2+K[2]^6+K[2]^4+1\right )^2}dK[1]+1\right )dK[2]+\int _1^x-\frac {K[1]}{K[1]^6+3 y(x)^2 K[1]^4+K[1]^4+3 y(x)^4 K[1]^2+2 y(x)^2 K[1]^2+y(x)^6+y(x)^4+1}dK[1]=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x/(x**6 + 3*x**4*y(x)**2 + x**4 + 3*x**2*y(x)**4 + 2*x**2*y(x)**2 + y(x)**6 + y(x)**4 - y(x) + 1) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out