3. The Laplace transform is not well suited to solving linear differential equat

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3. The Laplace transform is not well suited to solving linear differential equations with variable coefficients: nevertheless it can be used in some circumstances. Find the solutions of the differential equation ty"+ty'-+2y t that satisfies y(0) -0. Clearly specify the theorems used Hints: Let Y (s) Cty (t) (a) Show that Y(s) satisfies Y' (s) SO E s3 (s 1) s s 1 b Show the integrating factor is (c) Which leads to Y(s) (s 1)3 S S (d) Use partial fractions (or any other method) to solve for y(t). Note, using the convolution theorem is easier in this case.

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