The first order ODE is defined below.
    

Two solutions will be investigated (a) Natural solution ( no inflow) and (b) Forced Response due to a constant inflow of 0.3.  They are solved using numerical computation and the solutions are graphically presented.  The numerical integration of ODE's is based on Runge-Kutta type of numerical techniques.  These techniques require the DE's to be of first order (or a set of first order DE's).  They also require to the DEs to be arranged in state space form.  In this form only the first derivative is written on the left - the rest of the terms is on the right.

In general a m-th order ODE can be written as a set of m - first order equations.  The first order ODE can be naturally written in state space form as