Finding Laplace transform of a Differential Equation

[TheC0bbler]

Homework Statement

Consider the following initial value problem:

y''-6y'-7y=sin(9t)

y(0)=-4, y'(0)=-3

I need to solve for L[y(t)]

Homework Equations

The Attempt at a Solution

Here are the steps I've taken to solve it:

L(y'')-6L(y')-7L(y)=L(sin(9t))

s²L(y)-(-4)-(-3)-6(sL(y)-(-4))-7L(y)=9/(s²+81)

L(y)(s²-6s-7)-17=9/(s²+81)

L(y)(s²-6s-7)=9/(s²+81)+17

Y(s) =((9/(s²+81))+17)/(s²-6s-7)

I've simplified it with partial fractions as well but either way when I enter it into my homework page it says it's wrong.

 

[McAfee]

Not sure if the work is correct but you have to inverse the Laplace transform at the to solve.

 

[vela]

Recheck your Laplace transform of y''.