The general solution of the differential equation $x d y+\left(y-e^x\right) d x=0$ is :

where C is constant of integration

$x y-e^x=C$

$x d y+\left(y-e^x\right) d x=0$

$x d y+y d x-e^x d x=0$

integrating the eq

$\int x d y+y d x-\int e^x d x=0$

$\int d x y-\int e^x d x=0$

[as d(xy) = xdy - ydx   by product rule]

$x y-e^x-c=0$

$x y-c^x=c$