I'm trying to help this friend of mine over the internet on diff. equations. I understand the subject rather well but I'm stumped on this Inverse Laplace Transform.

What's the inverse laplace transform of -2s^2 ? I can't seem to find it on any table of laplace transform.

Here's the problem with my work.

Use the Laplace transform to solve

Work (that i'm explaining to him):

From the property 30 here.

Pauls Online Notes : Differential Equations - Table Of Laplace Transforms
Going back to the problem.

y(0) = 0

Mr F says: The mistake is in this line. The coefficient of Y' is -s^2 ....
It is the form :

(Linear).

Use the integrating factor method.

The solution is the form:

Take the inverse transform.

This is where I'm stuck... I need to take the inverse Laplace transform of:

, Where C is a constant.

After finding y(t) , I'll be able to find the constant...

Thanks.