Finding the Inverse Laplace Transformation

[izen]

Homework Statement

find the inverse laplace transformation of \frac{5s+4}{s^2} e^{-2s}

Homework Equations

The Attempt at a Solution

I have tried to partial fractions \frac{5s+4}{s^2} and I got \frac{5}{s}+\frac{4}{s^2} and I know that the answer must have u(t-2) because of second shifting ( a=2)

but I looked at the answer from this question is 5 u(t-2)(e^{4(t-2)} - e^{-(t-2)}).

I don't know how to get that answer please help

 

[vela]

The answer is wrong.

 

[izen]

so my answer is [5+4(t-2)] u(t-2) Is my answer right?
thank you

 

[Ray Vickson]

Homework Statement

find the inverse laplace transformation of \frac{5s+4}{s^2} e^{-2s}

Homework Equations

The Attempt at a Solution

I have tried to partial fractions \frac{5s+4}{s^2} and I got \frac{5}{s}+\frac{4}{s^2} and I know that the answer must have u(t-2) because of second shifting ( a=2)

but I looked at the answer from this question is 5 u(t-2)(e^{4(t-2)} - e^{-(t-2)}).

I don't know how to get that answer please help

First: what is the inverse Laplace transform of $(5s+4)/s^2$? Next: worry about the effect of the factor $e^{-2s}$.

 

[vela]

so my answer is [5+4(t-2)] u(t-2) Is my answer right?
thank you

Yes, that's correct.

 

[izen]

Thanks you all