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# Differential Equations/Laplace transforms - Differential Equations

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 =)

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)

TTYL, Abe

Differential Equations

Volunteer

#### 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