Need help solving non-homogeneous differential equation with Laplace

I'm trying to solve the following problem: g - (n/k) = dn/dt where g and k are constants and n(0) = 0. I decided to use Laplace to solve it since I like Laplace transforms a lot more. The problem is I get the solution n = gexp(-t/k) but the solution using the traditional ODE solving method gives me n = gk*(1-exp(-t/k)). What causes the discrepancies? It seems as if the Laplace is only giving me a partial solution.

On a related note, is there a way to write these equations out in a prettier format? New to Reddit and first post!