Answer Happy

Solve the following using laplace transform: 1. Ý" + 4y = f(t); y(0) = 1, y'(0) = 0, with f(t) ſo for 0 <t<4 3 for t > 4 = 2. 4" – 24 – 3y = f(t); y(0) = 1, y' (0) = 0, with So for 0 <t<4 f(t) for t > 4 = 12 3. 4" + 54' +6y = f(t); y(0) = y' (0) = 0, with S-2 for 0 <t<3 f(t) = for t > 3 0 4. y" – 4y + 4y = f(t); y(0) = -2, y(0) = 1, with f(t) = {i+2 for 0 <t<3 t + 2 for t > 3 1 5. g” +5 + 6 = 36(1 – 2) – 45(t – 5); g(0) = g (0) = 0 6. 4" – 4y' +13y = 48(t – 3); y(0) = y(0) = 0 y =Y 7. j" +16y' = 128(t – 57/8); y(0) = 3, y' (0) = 0 = 1 8. y" + 5y' + 6y = B8(t); y(0) = 3, y'(0) = = y = 0 9. y" – 3y' + 2y = ui(t), y(0) = 1, y (0) = 1, where ui(t) is unit step func- tion and ui(t) = u(t – 1). 1