Are these two inverse Laplace transform solutions equivalent?

[Jrlinton]

Homework Statement

Y=(8s-4)/(s²-4)

Homework Equations

The Attempt at a Solution

I rearranged the right side as:
8*(s/(s²-2²))-2*(2/(s²-2²))

Using the Laplace transform chart given in the class I was able to identify these as the transforms of hyperbolic sine and hyperbolic cosine making the inverse Laplace:
y=8cosh(2t)-2sinh(2t)
I checked this answer by working backwards and it all checks out but the worked out problem given by the instructor states the final answer as:
y=3e^(2t)-5e(-2t)=3[e][/2t]-5[e[/-2t]

I am wondering if these two solutions are equivalent?

 

[Jrlinton]

Correction: The given solution was y=3e^(2t)+5e(-2t).
I understand how he got this by using partial fractions, I would just like to know if the two functions are equivalent or if there was a mistake.

 

[Ray Vickson]

Correction: The given solution was y=3e^(2t)+5e(-2t).
I understand how he got this by using partial fractions, I would just like to know if the two functions are equivalent or if there was a mistake.

You do not need to ask us; you can work it out for yourself---and you should: that is how you will learn. Just expand sinh and cosh in terms of exp and see what you get.