a. [4 pts] Consider the initial value problem: y" - 4y'+8y=0 y(0) =0, y'(0) =1 Which of the following is the Laplace transform of the DE? OL ly} ($2 - 4 s+ 8) + (8 - s)y(0) + y'(0) of ly} ($2 - 45+ 8) + (4-s)y(0) - y'(0) OL ly} ($2 - 45 + 8) + (8-s)y(0) -y'(0) OLly} ($2 - 4s + 8) +(8 + s)y(0) - y'(0) b. [4 pts] Which of the following is the function Y (s) that needs to be inverted in order to solve the DE? OY (s ) = ( 8-2) 2 + 2 2 OY (s ) = 1 (s-1)2-22 or (s ) = 1 (s-1)+22 OY (s ) = ( s - 2 ) 2 + 12 c. [2 pts] Using the function Y (s) determined in the previous step, write down the solution of the initial value problem. (Note: decimal approximations are not acceptable.) IMPORTANT: Do not use the equation editor _ as results may be unpredictable (if you happen to select it, select it a second time to disable it). y (t ) =