Solve the following IVP using the Laplace Transform. Do not leave your answer in terms of...

- rs (ezetts Solution - Given I.V. p. y + y = gets y c) = 0 & Hat) = osti we ta King Laplace on both sides of egeraton 1. V.P. - L[ y' (A)] + L [year] = L [fees] ② know that L [y'(&)] - SY(S) - yed) where Y(S) = L [yees] Thus from s y 42-yco) + YES) = 5 es fets de = (&+1) 9 (4) – yes) = 60 Heldt (8 to 418) - = ē Elder (3+1) 4 (6) = we have - Si XI det to O S dt 1 78f1Y (2) a es 8

(8+1) 4(S) = 1-2 es 8 4 (8) = S18+) LLY (A)] = i-zes 2ės s(stu 8 18+1) e es s(s+1) [ [ + 1 - 2 L scat) S18+) = y(t) = { [sist 20L 1(8+1) = [[ - - 1 + 1, 1-21 L" (50] - • 1 - 0 + - 21 [ Sesto leas (8) =fltra) [-a) & a=1 to an Sest) Il stren] = l - et fees Now using Here F(8) = flat-a) = f(t-1)= 1- ect) ya) = let - 2 Jet-1) U (64) l-et-2 (1-et-D) U(A) yet = let yet) = l-et-all-eetly Ultry le Ulty is und step function as of Cehere