23.1.683 problem 678

Internal problem ID [5290]
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 : 678
Date solved : Tuesday, September 30, 2025 at 12:07:31 PM
CAS classification : [_exact, _rational]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

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

\[ -\frac {x^{3}}{3}+3 x y-\frac {y^{4}}{4}+c_1 = 0 \]

✓ Mathematica. Time used: 60.118 (sec). Leaf size: 1211

ode=(3 x-y[x]^3)D[y[x],x]==x^2-3 y[x]; 
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**2 + (3*x - y(x)**3)*Derivative(y(x), x) + 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out