Question

How do you calculate the explicit solution to dP/dt=kP-h?

Answer 1

Since the k and h are constants therefore this differential equation is a variable separable D.E. In order to solve this D.E. we need to group together terms with the same variable, that is, 

dP/(kP-h) =dt

perform integral on both sides of the equation, we obtain 


(1/k)* ln (kP - h) = t + C

Since we are not given limits to the equation, it is best to put C or the constant term in any side of the equation.