23.1.686 problem 681

Internal problem ID [5293]
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 : 681
Date solved : Tuesday, September 30, 2025 at 12:15:19 PM
CAS classification : [_exact, _rational]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 29

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

\[ -\frac {x^{4}}{4}-\frac {x^{2} y^{2}}{2}+x y-\frac {y^{4}}{4}+c_1 = 0 \]

✓ Mathematica. Time used: 60.147 (sec). Leaf size: 1807

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

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

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

Timed Out