32.4.5 problem Recognizable Exact Differential equations. Integrating factors. Example 10.741, page 90

Internal problem ID [5816]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 10
Problem number : Recognizable Exact Differential equations. Integrating factors. Example 10.741, page 90
Date solved : Sunday, March 30, 2025 at 10:18:38 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class C`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 103

ode:=y(x)^3+x*y(x)^2+y(x)+(x^3+x^2*y(x)+x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ y &= \frac {x^{2}+1}{\left (\sqrt {x^{2}+1}\, \sqrt {\frac {-1+\left (x^{4}+x^{2}\right ) c_1}{x^{2} \left (x^{2}+1\right )}}-1\right ) x} \\ y &= \frac {-x^{2}-1}{\left (\sqrt {x^{2}+1}\, \sqrt {\frac {-1+\left (x^{4}+x^{2}\right ) c_1}{x^{2} \left (x^{2}+1\right )}}+1\right ) x} \\ \end{align*}

✓ Mathematica. Time used: 3.821 (sec). Leaf size: 114

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

\begin{align*} y(x)\to -\frac {\sqrt {\frac {1}{x^3}} x \left (x^2+1\right )}{\sqrt {\frac {1}{x^3}} x^2-\sqrt {c_1 x^3-\frac {1}{x}+c_1 x}} \\ y(x)\to -\frac {\sqrt {\frac {1}{x^3}} x \left (x^2+1\right )}{\sqrt {\frac {1}{x^3}} x^2+\sqrt {c_1 x^3-\frac {1}{x}+c_1 x}} \\ y(x)\to 0 \\ \end{align*}

✗ Sympy

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

Timed Out