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

http://www.cramster.com/Answer-Board...7175008075.gif

Work (that i'm explaining to him):

http://www.cramster.com/Answer-Board...7175008075.gif

http://www.cramster.com/Answer-Board...0612501277.gif

http://www.cramster.com/Answer-Board...9362501405.gif

From the property 30 here.

Pauls Online Notes : Differential Equations - Table Of Laplace Transforms

http://www.cramster.com/Answer-Board...4050004624.gifhttp://www.cramster.com/Answer-Board...2800007106.gif

Going back to the problem.

http://www.cramster.com/Answer-Board...9362501405.gif

http://www.cramster.com/Answer-Board...6237507206.gif

y(0) = 0

http://www.cramster.com/Answer-Board...1862504628.gif

http://www.cramster.com/Answer-Board...9675007188.gif

http://www.cramster.com/Answer-Board...5300001622.gif

It is the form : http://www.cramster.com/Answer-Board...4675002571.gif (Linear).

Use the integrating factor method.

http://www.cramster.com/Answer-Board...4987501034.gifhttp://www.cramster.com/Answer-Board...1862505340.gif

The solution is the form:

http://www.cramster.com/Answer-Board...0300005587.gifhttp://www.cramster.com/Answer-Board...5300002488.gifhttp://www.cramster.com/Answer-Board...1862503976.gif

Take the inverse transform.

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

http://www.cramster.com/Answer-Board...9050005781.gif , Where C is a constant.

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

Thanks.