Please and thank you.

Solve by undetermined coefficients

y'' + 3y = -48x^{2}* e^{3x}

Find a linear operator that annihilates the given function, and verify

3 + e^{x}* cos2x

Inverse Laplace transforms of

(s + 1)^{3}/s^{4}

0.9s/((s - 0.1)(s + 0.2))

Use the Laplace transform to solve the given initial value problem

y'' + y' = 2^{1/2}sin2^{1/2}t y(0) = 10, y'(0)= 0

2y''' + 3y'' - 3y' - 2y = e^{-t}y(0)= 0, y'(0)= 0, y''(0)= 1

Evaluate the Laplace transform of

L[(1 - e^{t}+ 3e^{-4t})cos5t]

L^{-1}[(2s - 1)/(s^{2}(s^{2}+ 1)^{3})]

I'm sorry I don't have all of the symbols down yet.

edit: I solved a couple