83.8.2 problem 2

Internal problem ID [21955]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter III. First order differential equations of the first degree. Ex. IX at page 55
Problem number : 2
Date solved : Thursday, October 02, 2025 at 08:19:43 PM
CAS classification : [_rational]

\begin{align*} y^{3} \left (y y^{\prime }+x \right )&=\left (x^{2}+y^{2}\right )^{3} y^{\prime } \end{align*}

✗ Maple

ode:=y(x)^3*(x+y(x)*diff(y(x),x)) = (x^2+y(x)^2)^3*diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

Timed Out