# Thread: Laplace / inverse laplace transform

1. Problem: Find a (limited?) solution to the diff eq.

At the end of the solution, when you transform $\displaystyle \frac{-1}{s+1} + \frac{2}{s-3}$
why doesnt it become $\displaystyle -e^{-t} + 2e^{3t}$, t>0 ?

2.

3. That would be correct if the right hand side of the equation were 0. But the delta functions on the right mean that those are correct only for x greater than certain values so the step functions are needed.

What values are those and how are the step functions used?

5. Do you know what "$\displaystyle \delta(x)$" and "$\displaystyle \delta'(x)$" mean?