Show all your work. No points will be given to correct answers without reasonable work.

$(25$pts$.)$ Find the explicit solution of the initial value problem

$\frac{dy}{dx}+2y=x+e^{-2x},y(0)=0$

$(25$pts$.)$ Show that

$(-4e^{x}sin(y)+3y+e^{2x})dx+(3x-4e^{x}cos(y)+e^{2y})dy=0$

is an exact ordinary differential equation. Find the solution of the initial value problem if $y(0)=.$