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Use the Laplace transform?

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1 Answer

This si the amswer to your last question about (s2 -4s +7)/(s-1)4. Let's rewrite the numerator:

 s2 -4s +7 = s2 - 2s +1 -1 -2s +7 = (s-1)2 -2(s-1) + 4                (1)

If we divide (1) by (s-1) 4 we will  obtain:

            1/(s-1)2  - 2 /(s-1) 3  + 4/(s-1)4                                               (2)

But 1/(s-1) is a Laplace trabnform of the function [1/(n-1)! t n-1 et.

If you consequitively apply this formula for n = 2, 3, 4 you will come up with function

                                         y(t) = tet - t2 et +(2/3) t3 et