Question

A differential equation question:

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

Answer 1

Answer:

Step-by-step explanation:

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

We know that Laplace transform for

$t^n e^{at}$ is

$\frac{n!}{(s-a)^{n+1} }$, 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

$\frac{2!}{(s-4)^{2+1} } \\=\frac{2}{(s-4)^3}$