to find the inverse Laplace transform of the given function. F(s)=\frac{2^{n+1}n!}{s^{n+1}}

opatovaL

opatovaL

Answered question

2021-09-18

to find the inverse Laplace transform of the given function.
F(s)=2n+1n!sn+1

Answer & Explanation

delilnaT

delilnaT

Skilled2021-09-19Added 94 answers

Step 1: Consider the provided function,
F(s)=2n+1n!sn+1
Step 2: Further simplify,
Consider the function from the provided function is G(s)=n!sn+1
The inverse Laplace transform of the function G(s)=n!sn+1  is  g(t)=tn
So, G(s2)=2n+1n!sn+1=F(s)
Then,
L{g(2t)}=12G(s2)
2L{g(2t)}=G(s2)=F(s)
2g(2t)=L1{F(s)}
2(2t)n=L1{F(s)}=f(t)
f(t)=2n+1tn
Hence , the inverse Laplace transform is f(t)=2n+1tn

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?