with initial conditions of and
Partial Fraction Decomposition:
Equating like Coefficients:
Solving the system:
New Functions to take the inverse Laplace transform of:
Breaking down further:
Note: Completed the square on above
Now my problem is the middle term, I don't have any table entry at all for something like that, I have table entries for the first term and third term though. How would I break down the middle term further? Would really appreciate it if someone could help me finish this up, as it's been stumping me for a while now.
The answer in the book is:
Is all of my work thus far correct though?