2nd order of differential equations

Hi, I am studying for my final on Monday, 20th and I came across 4 questions on the 2nd order of differential equations that I couldn’t do. :( Please help me.

Problem #1: For what values of c do solutions $\displaystyle y"+cy'+y = 0$ have infinitely many zeros and tend to zero as t goes to infinity (here we are considering y as a function of t).

Problem #2: Solve the IVP: $\displaystyle y"-y = t, y(0) = 0, y'(0) = 0 $

Problem 3: For what values of w do solutions of $\displaystyle y"+9y = cos (wt)$ become unbounded as t goes to infinity. For what values of w are solutions periodic with a period of 3?

Problem #4: find the inverse Laplace Transform of the function $\displaystyle

e^{-10_s}\frac{2}{s^{2}+4}

$

thanks very much

Jen