Laplace transformation question

[John777]

Homework Statement

y''' - 5y'' + t^4 = 0

y(o) = y'(0)=0 y''(0)=1

The derivs are respect to t.

I converted everything into s and factored

Y(s) = (S^5+24)/(s^7(s+5) = A/s^7 + B/s^6 + C/s^5 + D/s^4 + E/s^3 + F/s^2 + G/s + H/(s+5)


Normally you would go through multiplying the terms by the denominator of each and setting s equal to a value that would cancel most things out. I can solve for H and A but after that each the method with which I discussed results in divide by zero error.

Any suggestions on what to do in this case?

 

[lippyka]

Homework Equations Laplace Transform of derivative is s multiplied by Laplace transform.The Attempt at a SolutionI tried to solve it in the same method mentioned earlier but that did not work out. I am thinking I may need to solve it using a linear algebra approach with matrices, but I am unsure how.