(4) [22pts.] Use the Laplace transform to solve the following initial-value problem: y 2y ...

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(4) [22pts.] Use the Laplace transform to solve the following initial-value problem: y" – 2y – 3y = g(t), y(0) = y'(0) = 0, where %3D - cos t if t< 3 9(t) = cos t + e2t if 3 <t (4) [22pts.] Use the Laplace transform to solve the following initial-value problem: y" – 2y – 3y = g(t), y(0) = y'(0) = 0, where %3D - cos t if t< 3 9(t) = cos t + e2t if 3 <t