29.24.17 problem 679

Internal problem ID [5270]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 24
Problem number : 679
Date solved : Tuesday, March 04, 2025 at 09:00:14 PM
CAS classification : [_rational]

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

✗ Maple

ode:=(x*a^2+y(x)*(x^2-y(x)^2))*diff(y(x),x)+x*(x^2-y(x)^2) = a^2*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.295 (sec). Leaf size: 48

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

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

✗ Sympy

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

Timed Out