Internal problem ID [3669]
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]
\[ \boxed {\left (x -{\mathrm e}^{x}\right ) y^{\prime }+\left (1-{\mathrm e}^{x}\right ) y=-x \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.094 (sec). Leaf size: 25
DSolve[(x-Exp[x])y'[x]+x Exp[x]+(1-Exp[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^x (x-1)+c_1}{e^x-x} \]