HELP LAPLACE TRANSFORM!!!!

Hey. My exam is in a few hours so it'd be cool if someone could show me this. I can guarantee you it won't hinder my understanding by just "giving me the answer"... nothing would benefit me more at this point haha.

Anyway. I don't even know if it's possible but can you find a Laplace transform of this in terms of :

It's part of a bigger question where I have to find the transfer function of the differential equation:

Assuming zero initial conditions: Hence my LHS is:

The transfer function is given by the ratio of the frequency-domain input to the frequency-domain output. The input being , and the output being .

In short I need to get on the RHS of that equation using the laplace transform integral I'd assume, and then manipulate the equation to get

(NOTE: are all constants.[/tex]

Many thanks.