s11_mthsc208_ws5c-LaplaceODE

s11_mthsc208_ws5c-LaplaceODE - MthSc 208 (Spring 2011)...

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Unformatted text preview: MthSc 208 (Spring 2011) Worksheet 5c MthSc 208: Differential Equations (Spring 2011) In-class Worksheet 5c: Solving ODEs with Laplace Transforms NAME: Consider the initial value problem: y - y = e2t , y(0) = 0, y (0) = 1. The following facts will be useful to solve this differential equation using Laplace transforms. (i) L{y (t)}(s) = s2 Y (s) - sy(0) - y (0) (ii) L{eat }(s) = 1 s-a 1. Take the Laplace transform of the initial value problem and solve for Y . 2. Use partial fraction decomposition to break up your equation for Y (s). Written by M. Macauley 1 MthSc 208 (Spring 2011) Worksheet 5c 3. Take the inverse Laplace transform (see (ii)) of each fraction to get the solution to the initial value problem. Written by M. Macauley 2 ...
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s11_mthsc208_ws5c-LaplaceODE - MthSc 208 (Spring 2011)...

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