Please help me with this test review for Dfferential equations

Consider the IVP given by y(4) - y = 0 with y(0) = 1, y'(0) = y"(0) = y(3)(0) = 0. H A 20 pts Use a characteristic equation to solve the IVP y(4) - y = 0 with y(0) = 1, y'(0) = y"(0) = y (3) (0) = 0. . PRINTED NAME: H B 20 pts Use power series to solve the IVP y(4) - y = 0 with y(0) = 1, y'(0) = y"(0) = y(3) (0) = 0. Hint: Use the initial conditions to find the constants do, a1, a2, a3 first which informs you about dan+1, dan+2, dan+3. It is OK to leave your answer as a power series, however I must have the pattern general for dan. Remember, you can check your work using Mathematica to sum your power series. I obtained y(x) = , [cos(x) + cosh(x)]. PRINTED NAME: H C 20 pts Use Laplace transforms to solve y(4) - y = 0 with y(0) = 1, y'(0) = y"(0) = y(3) (0) = 0. Hint: 1 S $4 - 1 4(s - 1) 4s(s + 1) 2 ($2 + 1 )