Question

find the inverse laplace transforms of
3s+7/s^2-2s-3
​

Answer 1

Answer:

I have to calculate the inverse Laplace Transform of this image:

F(s)=3s+7s2−2s−3

I try decomposing it in this way:

F(s)=3s−3+10(s−1)2−4=3s−1(s−1)2−4+52(s−1)2−4

where I can identify that the original function is

f(t)=3etcosh(2t)+5etsinh(2t)

But the textbooks says that the result should be: f(t)=−e−t+4e3t and I can't find where my mistake is.

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