Internal problem ID [2563]
Book: Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section: Chapter 11.3, page 316
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (1-x \right ) y^{\prime }-y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve((1-x)*diff(y(x),x)=x*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} {\mathrm e}^{-x}}{x -1} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 23
DSolve[(1-x)*y'[x]==x*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 e^{-x}}{x-1} \\ y(x)\to 0 \\ \end{align*}