Find inverse Laplace transform L^{-1}left{frac{s-5}{s^2+5s-24}right} Please provide supporting details for your answer

pedzenekO 2020-12-27 Answered
Find inverse Laplace transform L1{s5s2+5s24} Please provide supporting details for your answer
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Expert Answer

izboknil3
Answered 2020-12-28 Author has 99 answers
Step 1
The following formulae are used in solving the given problem.
L1f(x)+g(x)=L1(f(x))+L1(g(x))
L1(af(x))=aL1(f(x))
L1(1s+a)=eat
Step 2
Evaluate the inverse Laplace transform of the given function as follows.
L1{s5s2+5s24}=L1{211(s3)+1311(s+8)}( by partial fractions )
L1{211(s3)}+L1{1311(s+8)}
211L1{1(s3)}+1311L1{1s+8}
211e3t+1311e8t
Therefore, the inverse Laplace transform of the given function is 211e3t+1311e8t
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