How to Solve Non-Homogeneous Laplace Equations with Right-Hand Side Terms

[reece]

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 don't 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

 

[unplebeian]

After the second step you should get Y(s)= 8/((s-1)*(s+3)) + 2/(s+3)

After doing a partial fraction expansion you get Y(s)= 4/(s-1)

which should give you y(t)= ? (I think you can figure it out from here.)