1. ## double functioned differential

g is differentiable .
find the solution of
$y' + g'(x)y=g(x)g'(x)e^{-g(x)}$

g(x) could appear in the solution

how to approach it?

2. i pressume you want to solve for $y,$ so an integrating factor for the ODE is $g(x)$ multiply the equation and proceed, it's quite straightforward.

3. i was taught that the integrating factor is k=e^{g(x)}
$y'e^{g(x)} + g'(x)ye^{g(x)}=g(x)g'(x)$
$(ye^{g(x)})'=g(x)g'(x)$
$(ye^{g(x)})=\int g(x)g'(x) +c$

how to proceed
how i solve the right side

4. For the RHS, substitute u = g(x). Then du = g'(x) dx.