42Case Study 7: Approximating Series Solution to an ODE
42.1 Concepts and Analysis
A linear second‐order, initial value problem (IVP), ordinary differential equation (ODE) is 
. The initial conditions are 
and 
. In an ideal case the forcing function is a constant, held steady, for all x after the beginning at x0, 
. If 
it is a first‐order ODE, not second‐order. For 
, the analytical solution for this ODE is relatively simple (if one is practiced in solving ODEs) and results in a model of the form 
. There are three cases. In the case in which 
, the process is monotonic and asymptotically stable with τ‐values and . Then , , and .
If either or , the functional form of the solution is not the ...
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