Internal problem ID [3161]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 15
Problem number: 415.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (x -{\mathrm e}^{x}\right ) y^{\prime }+{\mathrm e}^{x} x +\left (1-{\mathrm e}^{x}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 21
dsolve((x-exp(x))*diff(y(x),x)+x*exp(x)+(1-exp(x))*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (x -1\right ) {\mathrm e}^{x}+c_{1}}{-x +{\mathrm e}^{x}} \]
✓ Solution by Mathematica
Time used: 0.101 (sec). Leaf size: 25
DSolve[(x-Exp[x])y'[x]+x Exp[x]+(1-Exp[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^x (x-1)+c_1}{e^x-x} \\ \end{align*}