Partial Fractions and Laplace Transforms for Third-Order and Higher Equations
I'm having some difficulty with some Laplace transforms and was wondering if someone could give me a helping hand.
I have some equations in the Laplace domain that I would like to put into the time domain. The equations I have are in the form of:
X(s)/Y(s) = (As^3 + Bs^2 + Cs + D) / (Es^4 + Fs^3 + Gs^2 + Hs + I)
I've done some revision of Laplace transforms but all the examples I see only go up to second order equations.
I take it that I will need to split up my equation using partial fractions and then put it into the time domain.
I'm not getting anywhere with these two steps.
Would someone be able to offer me some advice or a nudge in the right direction please? It would be most appreciated, I've been stuck for a while now.
Re: Partial Fractions and Laplace Transforms for Third-Order and Higher Equations
Can you factorize both numerator and denominator and use repeated applications of the convolution theorem? (There are formulas to factorize cubics and quartics into exact factors).