89.4.9 problem 10

Internal problem ID [24331]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 39
Problem number : 10
Date solved : Thursday, October 02, 2025 at 10:18:26 PM
CAS classification : [_exact, _rational]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 29

ode:=x^3+x*y(x)^2+y(x)+(y(x)^3+x^2*y(x)+x)*diff(y(x),x) = 0; 
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: 60.099 (sec). Leaf size: 1807

ode=( x^3+x*y[x]^2 +y[x] )+( y[x]^3+x^2*y[x] + x)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ 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