19. let y be the solution of the initial value problem +y = 6 cos cos 2x, dx y(0) = 3, y (0) = 1 let the laplace transform of y be f(s),then the value of f(1) i

Hi ankur,kindly refer the below image for your query thank you for asking

Let L(y) = F(s) = Y then, L(y") = (s^2)Y - sy(0) - y'(0) = (s^2)Y - 3s - 1 & L(y') = sY - y(0) = sY - 1 also, L(cosax) = s/(s^2 + a^2) => L(cos2x) = s/(s^2 + 4) now taking Laplace...