To solve the separable differential equation $$\frac{dy}{dx} + y\cos(x) = 3\cos(x) ,$$ we must find two separate integrals:
$\int$ $dy =$
and
$\int$ $dx =$
Solving for y we get that $y =$ (you must use k as your constant)
and find the particular solution satisfying the initial condition $$y(0) = 1.$$
$y(x) =$ .