So... Got my second diff eq test back today. 113/150.. Lost 31 points because it seems, contrary to my personal belief, I can't do Laplace transforms to save my life.
Therefore, I was hoping someone could help me. Here's the two functions I got very very wrong:


Some quick notes. Y = Laplace of y,U(t2) is that switch function that is zero when t < 2 and 1 when t>=2, and L = laplace transform
Here are my answers/ways I tried to solve them:
1.
It seems that is entirely wrong. I'm not sure why you can't do that and I would love some input.