4.15.48 (xey(x)+ex)y(x)+exy(x)+ey(x)=0

ODE
(xey(x)+ex)y(x)+exy(x)+ey(x)=0 ODE Classification

[_exact]

Book solution method
Exact equation

Mathematica
cpu = 0.0690978 (sec), leaf count = 33

{{y(x)c1exW(xec1exx)}}

Maple
cpu = 0.034 (sec), leaf count = 15

{y(x)ex+xey(x)+_C1=0} Mathematica raw input

DSolve[E^y[x] + E^x*y[x] + (E^x + E^y[x]*x)*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> C[1]/E^x - ProductLog[E^(-x + C[1]/E^x)*x]}}

Maple raw input

dsolve((exp(x)+x*exp(y(x)))*diff(y(x),x)+y(x)*exp(x)+exp(y(x)) = 0, y(x),'implicit')

Maple raw output

y(x)*exp(x)+x*exp(y(x))+_C1 = 0