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ODEHandout - ME360 Dynamic Systems Handout on ODEs Prof...

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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 brush-up will help prepare you for the Laplace Transform approach. Example ˙ x + 2 x = 4 · 1( t ) , x (0) = 5 (1) This is a first-order 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, so-called homogeneous equation

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