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Unformatted text preview: MthSc 208 (Spring 2011) Worksheet 5f MthSc 208: Differential Equations (Spring 2011) In-class Worksheet 5f: ODEs with Piecewise Forcing Terms
NAME: Consider the initial value problem y + y = f (t), y(0) = 0, y (0) = 1, where f (t) = 2t, 2, 0t1 t>1 1. Sketch f (t), and write it using the Heavyside function. 2. Take the Laplace transform of the differential equation, and solve for Y (s). Written by M. Macauley 1 MthSc 208 (Spring 2011) Worksheet 5f 3. Use partial fractions to decompose Y (s) into four terms. [Note: 1 1 1 = 2- 2 .] s2 (s2 + 1) s s +1 4. Apply the inverse Laplace transfrom to each term and write the solution to the IVP using the Heavyside function. 5. Write the solution as a piecewise function (i.e., not using the Heavyside function). Written by M. Macauley 2 ...
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