12.7.13 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 : Monday, January 27, 2025 at 05:32:36 AM
CAS classification : [_separable]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 27

DSolve[-y[x]+(x^4-x)*D[y[x],x]==0,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*}