
Simple Laplace Transform
Why is it that the seemingly easy equations are always the ones to stump you?
$\displaystyle \frac{dy}{dx}=y$ y=2 x=0 y_{0}=2
So y'=y
sL{y}y_{0}=y/s
sL{y}=(y/s)+y_{0}
L{y}=(y/s^{2})+(y_{0}/s)
I think I'm right so far, but I don't know what to do now, as I end up with:
$\displaystyle \frac{2}{s{^2}}+\frac{2}{s}$
And as
$\displaystyle \frac{2}{s{^2}}$ = $\displaystyle \frac{A}{s} + \frac{B}{s}$
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.