ME360  Dynamic Systems
Handout on ODEs
Prof. Gillespie  Fall 2010
ME360  Modeling, Analysis, and Control of Dynamical Systems  Fall 2010  Handout on ODEs
Solving differential equations may be something you haven’t done in a while. The following is intended as a quick
review. I offer pointers by going through a simple example and applyting the method involving the homogeneous
and particular solutions.
Note that this approach is not the only one available for solving ODEs.
You probably
encountered others in ME216. In fact, later in this class, we will be developing and applying an alternative method
involving the use of Laplace Transforms. In the end, all methods should produce the same solution.
I figure you are most familiar with the approach involving the homogeneous and particular solutions and a quick
brushup will help prepare you for the Laplace Transform approach.
Example
˙
x
+ 2
x
= 4
·
1(
t
)
,
x
(0) = 5
(1)
This is a firstorder differential equation. It is linear, with constant coefficients, or linear time invariant (LTI).
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 Fall '10
 Gillespie
 Complex number, RHS, homogeneous equation, characteristic equation, homogeneous solution, socalled homogeneous equation

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