Solve the following differential equations and initial value problems:
(a) y'''' + 4y'' - y' - 4y = 0
(b) y'''' + 4y'' - 3y' - 18y = 0
(c) y'''' + 6y'' + 12y' + 8y = 0
(d) y'''' + 4y'' - 7y' - 10y = 0, y(0) = -3, y'(0) = 12, y''(0) = -36
(e) y'''' + 4y'' - 7y' - 10y = 100x^2 - 64e^(3x), y(0) = -20, y'(0) = -29/5, y''(0) = 19/5
(f) y'''' - 5y'' - y' + 5y = 10x - 63e^(-2x) + 29sin(2x)
(g) y^(4) + 8y'' + 16y = 0, y(0) = -1, y'(0) = 5, y''(0) = -8, y'''(0) = -28
(h) y^(4) + 8y'' + 16y = 64xsin(2x)
(i) y^(4) + 2y''' - 2y' - y = 24xe^(-x) + 24e^x - 8sin(x), y(0) = -2, y'(0) = 0, y''(0) = 6, y'''(0) = 10
(j) y^(4) + 18y'' + 81y = 64xcos(x) + 108xcos(3x)