Hello everybody

I'm trying to solve the following differential equation derived from a first order kinetic process:

where

is the steady-state of

, that I guess, for the moment could be treated as a constant.

I know that the solution to the ODE is:

being

the initial condition.

I've tried to solve the equation with a piece of paper, but get stuck in the process. Im principle, this equation should be easily solved by separation of variables...

What I tried so far:

First, separation of variables

applying the integration limits:

solving the integral