Question

A differential equation question:

Find L\left \{ t^2e^4^t \right \}

Answer 1

Explanation:

To find Laplace transform of
`t^2e^4^t`

We know that Laplace transform for

`t^n e^(at)` is

`(n!)/((s-a)^(n+1) )`, for all n = 1,2,3.... and real values a..

Here n =2 and a=4

Hence substituting we get

Laplace transform of given term is

`(2!)/((s-4)^(2+1) ) \\=(2)/((s-4)^3)`