Question

(1 point) In this exercise we will use the Laplace transform to solve the following initial value problem: y" + 16 16, = { 10, 0<t<1 1<t , y(0) = 3, y'(0 = 4 (1) First, using Y for the Laplace transform of y(t), i.e., Y = L(y(t)), find the equation obtained by taking the Laplace transform of the initial value problem (2) Next solve for Y = (3) Finally apply the inverse Laplace transform to find y(t) y(t) = {

Answer 1

116, 03t<! g" +169 = 30 900-3, 9.004 ist Take capace transformation. Llyuly + 1624 ist s2yes) - syco)- y'(0) + 16466) = l'oest, 18dt to (52 +16) y(s) – 35-4 = est, L/216, ostel 6 (52+16) yes ) - 35-4 =- (52+16) y(s) - test :* + 3s +.4 408) E-sestre) + ss2016) * toate Take inverse capta ce transformtion Lifycay = 117.6 6527 +c' /sessit,'y + Y . & Et { $215 E . Ilk selle singt a g et? $(S211634 = 1,* singuide = // Cosqu To cos 4 + +to Sz to cos 464-1-, 21 To ostel le I ISCS from @ [Lyessy = y(t) = f To Los 4 (t-1), 11/61 +21 1 0 ostel - To Cosat tt +3 coset & singt.