I had this on a test today and can't get it out of my head.
I want to know if I got it right or wrong.
The question was to find the inverse Laplace transformation for the following:
$$\frac{\sqrt{\pi}}{\sqrt{s-3}}$$
My answer was $$\frac{1}{\sqrt{e^{3t}}}$$
However the more I think about it, I'm beginning to think it should be $$\sqrt{e^{3t}}$$
Please let me know which is right (if either of them).
Ok, so now I know I was incorrect in both cases. Now I want to understand where I went wrong in my process. I was using the the fact that the inverse transformation of $$\frac{\sqrt{\pi}}{\sqrt{s}}$$ is $$\frac{1}{\sqrt{t}}$$ Which would leave me with $$\frac{1}{\sqrt{t-3}}$$
Then I decided I'd apply the fact that the inverse transformation of $$\frac{1}{s-a}$$ is $$e^{at}$$
Which lead me to think $$\frac{1}{\sqrt{t-3}} = \sqrt{\frac{1}{t-3}} = \sqrt{e^{3t}} $$
NOTE
I'm not looking for another way to figure this inverse transformation out (after all someone has already posted the answer), I'm simply wanting to understand where I went wrong so I do not make this mistake again in the future (like on my final).
I figured it out! See answer below.