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Question
Find the inverse Laplace transform of"
F(s)=(9+s)/(4-s^2)

I am really struggling with completing my homework as well as grasping the whole Laplace transform...any help and explanation would be greatly appreciated! Thank you =)

Answer
Hello Laura,

Let me use IL for "Inverse Laplace"...

So, IL[(9+s)/(4-s^2)] = IL[(7/4)/(s+2)-(11/4*)/(s-2)], by expanding (9+s)/(4-s^2)
using partial fraction decomposition.

Thus, we get (by the linearity property of the inverse transform:
IL[(7/4)/(s+2)-(11/4*)/(s-2)] = IL[(7/4)/(s+2)] - IL[(11/4*)/(s-2)]
= (7/4)*IL[1/(s+2)] - (11/4)*IL[1/(s-2)]
= (7/4)*e^(-2t) - (11/4)*e^(2t)

OK?  Do you follow that?

TTYL, Abe

Differential Equations

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Abe Mantell

Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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