Transform the differential equation 9y+71y"-225y' - 1775y = 8e-t y(0) = 0 y'(0) = 0 y"(0) = 1 into an algebraic equation by taking the Laplace transform of each side. Use Y for the Laplace transform of y, (not Y(s)). 0-0 Therefore Y + s+7 Taking the inverse Laplace transform we get y

using Laplace transform, solve the equation below. y'' -2y' + 2y = cos (t)         y(0) = 1,  y'(0) = 0

How to solve the Laplace transform of the following equation: W(t)=cos(3t) - cos(7t) Please write answer clearly and show all steps.

(2s-8.4) find the inverse transform of s2+0.4s–0.21

Transform the differential equation into an algebraic equation by taking the Laplace transform of each side. Use Y for the Laplace transform of y, (not Y(s)). = Therefore Y +²7 + y = + s+7 s+8 Taking the inverse Laplace transform we get -0 2y" +22y" — 98y' — 1078y = 6e-8t y(0) = 0 y (0) = 0 y" (0) = 1

Find the fourier transform ↑ x(+) y (t) = x (+). Cos wot Y(f) = ? -fm fm f

(ii) -2t L[e Find the Laplace transform of sin2

3. (a) Calculate the Laplace transform of each function. Explain your reasoning (i) cos(2t) sin(4t). (ii) est cosh(3t). (iii) H(t-2) sin(4t-8). (iv) (t-3)²e-2tH(t-3).

Using Laplace transform solve the following shifted data IVP y' – 6y = 3(t + 5) y(-5) = -6

Q)find the inverse Laplace transform (3 L-' (P²t1) P-1 (4) L- 2P (P²-1)²