6.7.13 problem 13

Internal problem ID [1723]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page 91
Problem number : 13
Date solved : Tuesday, September 30, 2025 at 05:17:45 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

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

\[ y = \frac {c_1 \left (x -1\right )^{{1}/{3}} \left (x^{2}+x +1\right )^{{1}/{3}}}{x} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 27

ode=-y[x]+(x^4-x)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_1 \sqrt [3]{1-x^3}}{x}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.161 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x**4 - x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} \sqrt [3]{x^{3} - 1}}{x} \]