23.1.575 problem 568

Internal problem ID [5182]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 568
Date solved : Tuesday, September 30, 2025 at 11:50:22 AM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 51

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

\begin{align*} y &= \frac {1+\sqrt {2 c_1 \,x^{2}+2 x^{3}+1}}{x^{2}} \\ y &= \frac {1-\sqrt {2 c_1 \,x^{2}+2 x^{3}+1}}{x^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.421 (sec). Leaf size: 57

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

\begin{align*} y(x)&\to \frac {1-\sqrt {2 x^3+c_1 x^2+1}}{x^2}\\ y(x)&\to \frac {1+\sqrt {2 x^3+c_1 x^2+1}}{x^2} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*y(x)**2 + (-x**2*y(x) + 1)*Derivative(y(x), x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out