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