now all you have to do is find the constant coefficients, good luck.
In solving a problem, I ended up having to take the inverse laplace of (e^(-2s))/((x^2)(x-1))
I know what formula I need to use, but for some reason I'm stuck and can't remember how to do partial fractions with a denominator like that (I separated them so the numerator = 1), can anyone help?
That looks pretty standard to me. The partial fractions form is . Multiplying through by gives . Taking x= 0, . Taking x= 1, . Those are the only values of x that will reduce so simply but any other value for x will give a third equation. For example, taking x= 2, . Since we know that B= -1 and C= 1, that becomes or A= -1.
Another way to do any partial fractions, though harder since we are not taking advantage of those special values, x= 0 and x= 1, is to combine the fractions: .
Since this must be true for all x, we must have A+ C= 0, -A+ B= 0 and -B= 1. Again, we get B= -1, A= -1, and C= 1.
(Note that so Peritus' form is the same as mine.)