# Non-homogeneous laplace

Hi, I can solve homogeneous laplace fine, but with RHS i get stuck half way through.

Q:
y' +3y = 8e$$^{t}$$
y(0) = 2

Working as if it was homogeneous..

sY(s) - 2 + 3Y(s) = 8 . $$\frac{1}{s-1}$$
Y(s) (s+3) - 2 = 8 . $$\frac{1}{s-1}$$

I think the next step is
Y(s) = $$\frac{2}{s+3}$$ + $$\frac{8}{s-1}$$

and then do partial fractions but i dont think it leads me to where I need to be. I think i need to make it into a heaviside ??

Any help would be great. thanks