60.2.330 problem 908

Internal problem ID [10904]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 908
Date solved : Sunday, March 30, 2025 at 07:21:36 PM
CAS classification : [_rational]

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

✓ Maple. Time used: 0.029 (sec). Leaf size: 1345

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

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

✓ Mathematica. Time used: 10.427 (sec). Leaf size: 1065

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

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

✗ Sympy

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

Timed Out