The problem and attempt at solution are typed below
The solution of a linear differential equation as yours is the sum of the general solution of the homogeneous part (dP/dt+0.72P=0) and an arbitrary particular solution of the inhomogeneous equation. That solution can be for which dP/dt=0, that is P=const. Find that constant.
The solution of the homogeneous equation is of the form P=a eλt. Find λ.