Here's the question you clicked on:
Ciel_Phantomhive
inverse Laplace Transform F(s)= (s^2+2)/(s^2+2s+5)
no idea how to do this, but if you can find an answer it should match up with this http://www.wolframalpha.com/input/?i=inverse+laplace+%28s^2%2B2%29%2F%28s^2%2B2x%2B5%29
think it is partial fractions and then a formula, but really i should just shut up
Yeah but before the use of partial expansion you have to to make it a proper fraction.
Will it be (s^2+2)/(s+1)^2+4?
divide first \[\frac{s^2+2}{s^2+2s+5}=\frac{s^2+2s+5-2s-3}{s^2+2s+5}\] \[=1+\frac{-2x-3}{s^2+2x+5}\]
what did you divide by?
i just arranged it so that the power up top was less than the power in the denominator it is either that, or long division
it is just an algebra trick so you don't have to divide
added and subtracted what i needed to match up with the denominator
Oh okay Thanks
inverse laplace of 1 is the dirac delta - was that in the answer? Because if it wasn't then you may have added a solution...
Oh I have forgotten that, thanks
Ah, yes. I just looked at the Wolfram|Alpha link. It did indeed have the delta function.
yeah it is in there, rest looks like greek
Well the rest falls out of all of that fun stuff from DE class that I don't remember...
i know you use partial fractions, and then tables i think
but this is when i really should shut up, because i have no idea, although it seems like something i ought to learn
I'm pretty sure OP is familiar with relations such as \[\mathcal{L}^{-1}\{\frac{1}{s^n}\} = \frac{t^{n-1}}{\Gamma (n)}\]But yeah the hard part is just the setup, the rest is looking at the table!