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
and applying exponential to both sides of the equation leads to:
finally, solving for
which is almost the solution, but the exponential is raised to and not to as it should be.
I would appreciate if somebody would point out where is the mistake in the calculation