Can someone double check my solution to this Laplace Transform problem?

[EaglesFan7]

Homework Statement

Who can check my work for this problem? I tried to use an online laplace calculator to verify my answer but it didn't support finding laplace examples with heavyside

Relevant Equations

Laplace of h(t-c)*f(t-c)=e^(-cs)*F(s)

My solution is in the file shown here

 

[jedishrfu]

Can you type this in with latex in the future? It’s a good skill to know and makes it a lot easier to read than the sepia photo provided.

Is there any way to work the problem backwards to get your original results? That would be a good check.

 

[petercole]

I checked and little confused about that. If someone checked this homework problem, then also let me know by mentioning me on that thread.

 

[SammyS]

Here's one that's somewhat more readable. (I should have cropped it a bit.)

 

[DaveE]

One of the problems with asking for free help is that we (OK, I) have a limited amount of patience. I do know about Laplace transforms, but I find your question really really confusing. What's u₂(t)? Where did the "t-2" come from? What really was the homework question?
People often say "there is no such thing as a bad question". They are wrong. I am 99.99% sure I know the answer, but I don't want to solve the riddle of what was the question.
Maybe someone else will take up the challenge, even though the first 4 people aren't giving you the answer you seek.

 

[vela]

What's u2(t)? Where did the "t-2" come from?

I ran across this notation awhile back, and it was unfamiliar to me at the time as well. It probably didn't help that the OP translated it into $h-2$, whatever that's supposed to mean. Anyway, some people denote $u(t-c)$, where $u(t)$ is the unit step function, by $u_c(t)$.