Question: 3. (Gradable). Solve the following ODEs using the Laplace transform (Taken from Boyce DiPrima Chapter 6.2: Solution of Initial Value Problems). (a) y(4) - y

3. (Gradable). Solve the following ODEs using the Laplace transform (Taken from Boyce DiPrima Chapter 6.2: Solution of Initial Value Problems). (a) y(4) - y =0;y(0) = 1,y'(0) = 0,y"(0) = 1,y" (0) = 0. (b) y(4) - Ay = 0;y(0) = 1,y'(0) = 0,y"(0) = -2,1(0) =0. (c) y" twy =0,w / 4;y(0) = 1,y'(0) =0. (d) y" - 2y' + 2y = cost; y(0) = 1, y'(0) = 0. (e) y" - 2y' + 2y = e ;y(0) = 0,y'(0) = 1. (f) y" + 2y' + y = de t; y(0) = 2.7'(0) = -1

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