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Laplace transform of Power function

Hello,

I was trying to use Wolfram Alpha engine to transform a power function using laplace transform and then inverse using inverse laplace transform.

The function is:

D(t) = a*t^b + c

('t' is the initial variable, 's' is the transform variable and 'a', 'b', and 'c' are constant parameters)

When I transfer it using Laplace Transform, I got this results:

a s^(-b-1) Gamma(b+1)+c/s

However, when I try to inverse the result function using the formula: 1/s^2 as shown below:

1/[s^2*(a s^(-b-1) Gamma(b+1)+c/s)]

The engine doesn't give me any results. as shown in the below image:

enter image description here

I keep clicking on 'Solve' button but with no response.

Can anyone help me in finishing this?

Thank you..

POSTED BY: Mohammed Sadeq
2 Replies
POSTED BY: Mohammed Sadeq

What result are you expecting for the Inverse Laplace Transform of 1/[s^2*(a s^(-b-1) Gamma(b+1)+c/s)]?

It doesn't show a result becuase it doesn't find any result.

Are you sure you're not looking for the inverse transform of (1/s^2)(a s^(-b-1) Gamma(b+1)+c/s) instead? Are you looking for the convolution of t and a*t^b + c?

POSTED BY: Sean Clarke
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