I guess I found it now. Again so easy that you don't see it because you are looking for far more complicated things....
Solve the following differential equation :
x' = hx + b
if you know that if
Actually I'm only allowed to use the method of separating the values.
I found the solution but with another way which I'm in fact not supposed to know...
Maybe somebody knows the asked method for this... or at least how I could transform it in something like:
x' = f(x) * g(t)