38.2.10 problem 10

Internal problem ID [6439]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 10
Date solved : Sunday, March 30, 2025 at 10:59:56 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.029 (sec). Leaf size: 23

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

\[ y = \operatorname {RootOf}\left (x c_1 \,\textit {\_Z}^{4}-c_1 x -\textit {\_Z} \right )^{2} x \]

✓ Mathematica. Time used: 60.158 (sec). Leaf size: 1659

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

Timed Out