Question: Please help with Laplace Transform, Thank you! Let 7 + 3+ + 2r =e , x(0) =0, x(0) =0. The Laplace Transform of r(t) is

Please help with Laplace Transform, Thank you!

Please help with Laplace Transform, Thank you!
Let 7 + 3+ + 2r =e ", x(0) =0, x(0) =0. The Laplace Transform of r(t) is 1 C {x(t)} = ($2 + 3s + 2) (8 + 4) (a) Find the partial fraction decomposition for C{r(t) }. (b) Write C {x(t)} as a product of three known Laplace Transforms. (c) Write C {r(t)} as the Laplace Transform of two convolutions. Note: (f *g) *h = f * (g *h) = f *g*h. That is, convolution is associative. It is also commutative, so f * g =g *h. (d) Find r(t)

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