Question

(1 point) Consider the initial value problem d'y dy dt2 dt dt Write down the Laplace transform of the left-hand side of the equation given the initial conditions Your answer should be a function of s and Y with Y denoting the Laplace transform of the solution y Write down the Laplace transform of the right-hand side of the equation Your answer should be a function of s only. Next equate your last two answers and solve for Y. You have Your answer should be a function of s only. Finally take the inverse laplace transform of your third answer to obtain the solution of the given initial value problem. y(t) = Your answer should be a function of t.

Answer 1

2t Simitontly dk -Ata 人ナ2 st3 St 1 2 ん+2 ん·13 K43

ab .at M CA 亼-3 +2)-2 2 -t A+2 づ-3 3 5 t 2 4 25 32 나

2t 3 nt S 25 S 25で -t 2. ns