# Math Help - [SOLVED] Can Anyone help solve this one?

1. ## [SOLVED] Can Anyone help solve this one?

Any help appreciated

2. part i:

$y''+6y'+8y=40$

$p^{2}Y-py(0)-y'(0)+6(pY-y(0))+8Y=\frac{40}{p}$

Using the initial conditons y'(0)=0 and y(0)=0:

$Y(p^{2}+6p+8)=\frac{40}{p}$

$Y=\frac{5}{p+4}-\frac{10}{p+2}+\frac{5}{p}$

Use the inverse Laplace for each and get:

$y=5e^{-4t}-10e^{-2t}+5$