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Hi I just have a problem in regards to setting up your partial fractions when doing nonhomogeneous differential equations using Laplace transforms.

I’m at the stage of getting the inverse Laplace of: (1-625S^4)/(S^3 (25S^2+1) )

2. Relevant equations

3. The attempt at a solution

So I’m going to simplify that equation by using partial fractions and I get:

A/S+B/S^2 +C/S^3 +(DS+E)/(25S^2+1)

I roughly understand repeated linear factors but however I’m having trouble grasping why there is an S attached to the D. If you could explain to me why this occurred that would be very helpful thanks in advance.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Partial fractions question.

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