60.2.384 problem 962

Internal problem ID [10958]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 962
Date solved : Sunday, March 30, 2025 at 07:32:40 PM
CAS classification : [_rational]

\begin{align*} y^{\prime }&=\frac {4 x \left (a -1\right ) \left (a +1\right ) \left (-y^{2}+a^{2} x^{2}-x^{2}-2\right )}{-4 y^{3}+4 a^{2} x^{2} y-4 x^{2} y-8 y-a^{2} y^{6}+3 a^{4} y^{4} x^{2}-6 y^{4} a^{2} x^{2}-3 a^{6} y^{2} x^{4}+9 y^{2} a^{4} x^{4}-9 y^{2} a^{2} x^{4}+a^{8} x^{6}-4 a^{6} x^{6}+6 a^{4} x^{6}-4 a^{2} x^{6}+y^{6}+3 x^{2} y^{4}+3 x^{4} y^{2}+x^{6}} \end{align*}

✓ Maple. Time used: 0.066 (sec). Leaf size: 79

ode:=diff(y(x),x) = 4*x*(a-1)*(a+1)*(-y(x)^2+a^2*x^2-x^2-2)/(-4*y(x)^3+4*a^2*x^2*y(x)-4*x^2*y(x)-8*y(x)-a^2*y(x)^6+3*a^4*y(x)^4*x^2-6*y(x)^4*a^2*x^2-3*a^6*y(x)^2*x^4+9*y(x)^2*a^4*x^4-9*y(x)^2*a^2*x^4+a^8*x^6-4*a^6*x^6+6*a^4*x^6-4*a^2*x^6+y(x)^6+3*x^2*y(x)^4+3*x^4*y(x)^2+x^6); 
dsolve(ode,y(x), singsol=all);
 

\[ -\frac {y}{\left (a -1\right ) \left (a +1\right )}+\frac {2}{\left (a^{2}-1\right )^{2} \left (a^{2} x^{2}-x^{2}-y^{2}\right )^{2}}-\frac {2}{\left (a^{2}-1\right )^{2} \left (a^{2} x^{2}-x^{2}-y^{2}\right )}+c_1 = 0 \]

✓ Mathematica. Time used: 3.615 (sec). Leaf size: 1743

ode=D[y[x],x] == (4*(-1 + a)*(1 + a)*x*(-2 - x^2 + a^2*x^2 - y[x]^2))/(x^6 - 4*a^2*x^6 + 6*a^4*x^6 - 4*a^6*x^6 + a^8*x^6 - 8*y[x] - 4*x^2*y[x] + 4*a^2*x^2*y[x] + 3*x^4*y[x]^2 - 9*a^2*x^4*y[x]^2 + 9*a^4*x^4*y[x]^2 - 3*a^6*x^4*y[x]^2 - 4*y[x]^3 + 3*x^2*y[x]^4 - 6*a^2*x^2*y[x]^4 + 3*a^4*x^2*y[x]^4 + y[x]^6 - a^2*y[x]^6); 
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**2*x**2 - x**2 - y(x)**2 - 2)/(a**8*x**6 - 4*a**6*x**6 - 3*a**6*x**4*y(x)**2 + 6*a**4*x**6 + 9*a**4*x**4*y(x)**2 + 3*a**4*x**2*y(x)**4 - 4*a**2*x**6 - 9*a**2*x**4*y(x)**2 - 6*a**2*x**2*y(x)**4 + 4*a**2*x**2*y(x) - a**2*y(x)**6 + x**6 + 3*x**4*y(x)**2 + 3*x**2*y(x)**4 - 4*x**2*y(x) + y(x)**6 - 4*y(x)**3 - 8*y(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out