89.4.21 problem 22

Internal problem ID [24343]
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 : 22
Date solved : Thursday, October 02, 2025 at 10:20:40 PM
CAS classification : [_rational]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 32.999 (sec). Leaf size: 3604

ode:=y(x)*(x^3*y(x)^3+2*x^2-y(x))+x^3*(x*y(x)^3-2)*diff(y(x),x) = 0; 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\begin{align*} \text {Expression too large to display} \\ \text {Expression too large to display} \\ \end{align*}

✗ Mathematica

ode=y[x]*( x^3*y[x]^3 +2*x^2 -y[x]   )+x^3*( x*y[x]^3 -2 )*D[y[x],x]==0; 
ic={y[1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*(x*y(x)**3 - 2)*Derivative(y(x), x) + (x**3*y(x)**3 + 2*x**2 - y(x))*y(x),0) 
ics = {y(1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out