25.1.21 problem 21

Internal problem ID [4233]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 21
Date solved : Monday, January 27, 2025 at 08:43:19 AM
CAS classification : [_separable]

\begin{align*} \left (1-x \right ) y^{\prime }&=y x \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 15

dsolve((1-x)*diff(y(x),x)=x*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {c_{1} {\mathrm e}^{-x}}{x -1} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 23

DSolve[(1-x)*D[y[x],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*}