Laplace of a Differential Equation

I'm trying to solve the problems from this project:

http://www.cengage.com/math/book_content/0495108243_zill/projects_archive/de8e/Project7.pdf"

I already did problem # 1, and now I'm trying to solve problem # 2, which will help me to solve problem # 3.

Solve the differential equation using the Laplace Transform:

http://tinypic.com/r/sq1ait/3"

Knowing that

http://tinypic.com/r/50pkt2/3"

So, what I did was that I plugged in the 2nd equation into the 1st equation, took the Laplace...and I got http://i27.tinypic.com/34glqbq.jpg"

I'm stuck here because I don't know what to do with the T(0) and the S's ...

I appreciate any help, thank you!

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