I don't really understand how to start this question, can anyone help please?

For $\displaystyle n \in Z$ with $\displaystyle n \geq 0$, the Laguerre differential equation

$\displaystyle

t\frac{d^2f}{dt^2}+(1-t)\frac{df}{dt}+nf=0

$

Has the solution $\displaystyle L_n(t)$ for which $\displaystyle L_n(0)=n!$

Prove that the Laplace tranform on $\displaystyle L_n(t)$ is $\displaystyle \frac{n!(s-1)^n}{s^{n+1}}$

Hence find the Laplace transform of $\displaystyle tL_n(t)$ and deduce the value of

$\displaystyle

\int^\infty_0e^{-2t}tL_n(t)dt

$

Can someone please help me or even give me a push in the right direction, please, I'm really really stuck!! I have spent days trying to make a start but I really don't understand where to start!!!