78.4.3 problem 3

Internal problem ID [18055]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 8 (Exact Equations). Problems at page 72
Problem number : 3
Date solved : Monday, March 31, 2025 at 05:01:00 PM
CAS classification : [_exact, _rational]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

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

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

✓ Mathematica. Time used: 60.162 (sec). Leaf size: 1210

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

Timed Out