89.4.15 problem 16

Internal problem ID [24337]
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 : 16
Date solved : Thursday, October 02, 2025 at 10:19:03 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class C`]]

\begin{align*} \left (x^{2} y^{2}-1\right ) y+x \left (x^{2} y+2 x +y\right ) y^{\prime }&=0 \end{align*}

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

Timed Out