[22pts.] Use the Laplace transform to solve the initial-value problem: y +3y' 4y = g(t),...

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[22pts.] Use the Laplace transform to solve the initial-value problem: y" +3y' – 4y = g(t), y(0) = 0, y(0) = 1, where t if t<7 g(t) = 2t if 7<t (Hint: it is better to express g(t) in terms of unit step function.) [22pts.] Use the Laplace transform to solve the initial-value problem: y" +3y' – 4y = g(t), y(0) = 0, y(0) = 1, where t if t<7 g(t) = 2t if 7<t (Hint: it is better to express g(t) in terms of unit step function.)