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**Lancet** In the course of working a 2nd order ODE with initial conditions, I ended up with this part of what I needed to get the inverse Laplace transform of:

$\displaystyle \frac{1}{(s - 2)^2}$

Now, the textbook did this:

$\displaystyle t^n e^{at} = \frac{n!}{(s - a)^{n + 1}}$

$\displaystyle n = 1, a = 2$

$\displaystyle L^{-1} = te^{2t}$

But this is what I did:

$\displaystyle e^{at} = \frac{1}{s - a}$

$\displaystyle (e^{at})^2 = \left[\frac{1}{s - a}\right]^2 = \frac{1}{(s - a)^2}$

$\displaystyle L^{-1} = e^{4t}$

These two answers don't look equivalent, but what I did looks like it should work. So, why is it wrong?