26.4.15 problem Recognizable Exact Differential equations. Integrating factors. Exercise 10.7, page 90

Internal problem ID [6961]
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. Exercise 10.7, page 90
Date solved : Tuesday, September 30, 2025 at 04:07:19 PM
CAS classification : [_rational]

\begin{align*} x^{4} y^{2}-y+\left (x^{2} y^{4}-x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 25

ode:=x^4*y(x)^2-y(x)+(x^2*y(x)^4-x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ -\frac {x^{3}}{3}-\frac {1}{x y}-\frac {y^{3}}{3}+c_1 = 0 \]

✓ Mathematica. Time used: 60.093 (sec). Leaf size: 1507

ode=(x^4*y[x]^2-y[x])+(x^2*y[x]^4-x)*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**4*y(x)**2 + (x**2*y(x)**4 - x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out