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o-na [289]
3 years ago
10

Use appropriate algebra and theorem 7.2.1 to find the given inverse laplace transform. (write your answer as a function of t.) ℒ

−1 s s2 + 3s − 4
Mathematics
1 answer:
castortr0y [4]3 years ago
4 0

We assume you want to find the inverse transform of s/(s^2 +3s -4). This can be written in partial fraction form as

(4/5)/(s+4) + (1/5)/(s-1)

which can be found in a table of transforms to be the transform of

(4/5)e^(-4t) + (1/5)e^t


_____

There are a number of ways to determine the partial fractions. They all start with factoring the denominator.

s^2 +3x -4 = (s+4)(s-1)


After that, you can postulate the final form and determine the values of the coefficients that make it so. For example:

A/(s+4) + B/(s-1) = ((A+B)s + (4B-A))/(s^2 +3x -4)


This gives rise to two equations:

(A+B) = 1

(4B-A) = 0

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