1. ## Simple Laplace Transform

Why is it that the seemingly easy equations are always the ones to stump you?

$\frac{dy}{dx}=-y$ y=2 x=0 y0=2

So y'=-y

sL{y}-y0=-y/s

sL{y}=(-y/s)+y0

L{y}=(-y/s2)+(y0/s)

I think I'm right so far, but I don't know what to do now, as I end up with:

$\frac{-2}{s{^2}}+\frac{2}{s}$

And as

$\frac{-2}{s{^2}}$ = $\frac{A}{s} + \frac{B}{s}$

I end up with

-2=As+Bs

and can't see my next (any) move from there.

Please tell me I've made a stupid mistake I'm not aware of earlier in the equation. Any help is much appreciated.