find the inverse Laplace transform of the given function. {F}{left({s}right)}=frac{{{2}{s}-{3}}}{{{s}^{2}-{4}}}

floymdiT

floymdiT

Answered question

2021-02-16

find the inverse Laplace transform of the given function.
F(s)=2s3s24

Answer & Explanation

SabadisO

SabadisO

Skilled2021-02-17Added 108 answers

Step 1
Given function is:
F(s)=2s3s24
Since the Laplace transform of:
L(sinhat)=as2a2
And
L(coshat)=ss2a2
Step 2
Now,
Using the above transform:
F(s)=2s3s24
=2ss243s24
=2ss222322s222
=2L(cosh2t)32L(sinh2t)
=L(2cosh2t32sinh2t)
inverse Laplace transform of L(2cosh2t32sinh2t):
L1(L(2cosh2t32sinh2t))=2cosh2t32sinh2t
THEREFORE Inverse Laplace transform of given function is 2cosh2t32sinh2t

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Differential Equations

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?