88.8.9 problem 9

Internal problem ID [24017]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 44
Problem number : 9
Date solved : Thursday, October 02, 2025 at 09:54:16 PM
CAS classification : [_rational]

\begin{align*} x^{2} y+\left (x^{2}-y^{2}\right ) y^{\prime }&=0 \end{align*}

✗ Maple

ode:=x^2*y(x)+(x^2-y(x)^2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=( x^2*y[x] )+( x^2-y[x]^2 )*D[y[x],{x,1}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

Timed Out