Obtain the Laplace Transform of Lleft{e^{-2x}+4e^{-3x}right}

Question
Laplace transform
asked 2021-03-18
Obtain the Laplace Transform of \(L\left\{e^{-2x}+4e^{-3x}\right\}\)

Answers (1)

2021-03-19
Step 1
Laplace Transform: The Laplace transform provides an effective tool or way of solving initial-value problems for linear differential equations with constant coefficients. The type of problem differs accordingly with the question.
Step 2
The formula for calculating Laplace transform of \(e^{ax}=\frac{1}{(s-a)}\)
According to the question: \(L(e^{-2x} +4e^{-3x})\) we can separate the two terms
\(L(e^{-2x})=\frac{1}{(s+2)}\)
\(L(e^{-3x})=\frac{1}{(s+3)}\)
\(=\frac{1}{(s+2)}+\frac{4}{(s+3)}\)
\(=\frac{(s+3+4s+8)}{(s+2)(s+3)}\)
\(=\frac{(5s+11)}{(s+2)(s+3)}\)
\(=\frac{(5s+11)}{(s^2+3s+2s+6)}\)
\(=\frac{(5s+11)}{(s^2+5s+6)}\) is the answer.
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