29.15.7 problem 415

Internal problem ID [5013]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 415
Date solved : Monday, January 27, 2025 at 10:03:34 AM
CAS classification : [_linear]

\begin{align*} \left (x -{\mathrm e}^{x}\right ) y^{\prime }+x \,{\mathrm e}^{x}+\left (1-{\mathrm e}^{x}\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

dsolve((x-exp(x))*diff(y(x),x)+x*exp(x)+(1-exp(x))*y(x) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.114 (sec). Leaf size: 25

DSolve[(x-Exp[x])D[y[x],x]+x Exp[x]+(1-Exp[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^x (x-1)+c_1}{e^x-x} \]