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
Answer & explanation
Correct answer: option 4
$x d y+\left(y-e^x\right) d x=0$
$x d y+y d x-e^x d x=0$
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]
$x y-e^x-c=0$
$x y-c^x=c$