Internal problem ID [1073]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {-y+\left (x^{4}-x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(-y(x)+(x^4-x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (x -1\right )^{\frac {1}{3}} \left (x^{2}+x +1\right )^{\frac {1}{3}}}{x} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 27
DSolve[-y[x]+(x^4-x)*y'[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*}