23.1.685 problem 680

Internal problem ID [5292]
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 : 680
Date solved : Tuesday, September 30, 2025 at 12:11:53 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _dAlembert]

\begin{align*} \left (x^{3}+y^{3}\right ) y^{\prime }+x^{2} \left (a x +3 y\right )&=0 \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 29

ode:=(x^3+y(x)^3)*diff(y(x),x)+x^2*(a*x+3*y(x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\operatorname {RootOf}\left (a \,x^{4} c_1^{{4}/{3}}+4 x^{3} c_1 \textit {\_Z} +\textit {\_Z}^{4}-1\right )}{c_1^{{1}/{3}}} \]

✓ Mathematica. Time used: 60.1 (sec). Leaf size: 1430

ode=(x^3+y[x]^3)D[y[x],x]+x^2(a x+3 y[x])==0; 
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") 
a = symbols("a") 
y = Function("y") 
ode = Eq(x**2*(a*x + 3*y(x)) + (x**3 + y(x)**3)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out