Solve the following problem:
Find y as a function of x if...
1a) (x^2)y" - 5xy' - 27y = x^7 w/ y(1) = 4, y'(1) = 6
1b) y'''-11 y'' + 18 y' = 0 w/ y(0) = 1, y'(0) = 3, y"(0) = 4
1c) y''' +49 y' = 0 w/ y(0) = -6, y'(0) = -42, y''(0) = 147
1d) y^(4) - 4 y''' + 4 y'' = 0 w/ y(0) = 1, y'(0) = 4, y''(0) = 4, y'''(0)=0
1e) y''' -2 y'' -y'+2 y = 0 w/ y(0) = 8, y'(0) = 1, y''(0) = -1
1f) y'''- 11 y'' + 28 y' = 54 e^x w/ y(0) = 25, y'(0) = 24, y''(0) = 26
1g) y^(4) - 12 y''' + 36 y'' = -256 e^{-2x}, w/ y(0) = 12, y'(0) = 4, y''(0) = 32, y'''(0)=8.
1h) If L = D^2 + 3xD - 4x and y(x) = 2x-3e^(5x), then Ly = ? Find Ly
Provide step by step calculations.