Find the function g such that the function f defined by the integral expression *cos(67) g(t T) dr, f(t) = c has the Laplace Transform F(s) = L[f(t)] is given by F(s) = == 8 (82+36)((8-2)+25) g(t) = = Consider the non-homogeneous problem with zero initial data and arbitrary source function g. y"-9y+20y= g(t), y(0) = 0, y'(0) = 0. a. (3/10) Find the function H such that the Laplace Transform of solution, Y = C[y], can be written as Y(s) = H(s) G(s), where G = C[g], H(s) = b. (7/10) Find the function h such that the solution y of the IVP above has the form y=h*g. h(t) = Consider the non-homogeneous problem with zero initial data and arbitrary source function g. y" 10 y' +41 y = g(t), y(0) = 0, y'(0) = 0. == a. (3/10) Find the function H such that the Laplace Transform of solution, Y can be written as Y(s) = H(s) G(s), where G = L[g]. H(8) = ====== Ly b. (7/10) Find the function h such that the solution y of the IVP above has the form y=h* g. h(t)=