I was recently given a question to solve by my professor that required me to find the Inverse Laplace. I’m sure my solution was correct but I’m wondering if my professors solution is also correct.

My professor and I both manage to start off the problem the same way but as soon as we get to partial fractions our work begins to differ. I want to include that I do understand what my professor did to get the answer he did. He used the formula for partial fraction expansion and inverse shown below. I just want to know if both answers are somehow equivalent to one another because I’m having trouble seeing whether or not they are and if so, is one way preferred to the other because my solution was the method originally taught to me. Thank you.

The question: Q

My Solution: Solution

Professors Solution:Prof Solution

Expansion and Inverse formula:Formula