23.2.160 problem 163

Internal problem ID [5515]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 163
Date solved : Tuesday, September 30, 2025 at 12:46:06 PM
CAS classification : [_rational]

\begin{align*} x^{2} {y^{\prime }}^{2}+x \left (x^{2}+x y-2 y\right ) y^{\prime }+\left (1-x \right ) \left (x^{2}-y\right ) y&=0 \end{align*}

✗ Maple

ode:=x^2*diff(y(x),x)^2+x*(x^2+x*y(x)-2*y(x))*diff(y(x),x)+(1-x)*(x^2-y(x))*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=x^2 (D[y[x],x])^2+x(x^2+x y[x]-2 y[x])D[y[x],x]+(1-x)(x^2-y[x])y[x]==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*Derivative(y(x), x)**2 + x*(x**2 + x*y(x) - 2*y(x))*Derivative(y(x), x) + (1 - x)*(x**2 - y(x))*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out