Find the inverse Laplace transform for the following:
a. $F(s) = \dfrac{{2s - 3}}{{{s^2} - 3s + 2}}$.
I used partial fractions and I ended up getting
$$y(t) = {e^t} + {e^{2t}}.$$
b. $F(s) = \dfrac{{{e^{ - 2s}}}}{{s - 9}}$.
I ended up getting $e^{9t-9} h(t-2)$ and $0$ being $\neq 2$.
Hints:
a). is correct
b.) is incorrect - think about the $t$ term and that being $(t-2)$ in the exponential (you got the Heaviside portion correct, so it is close).
It should be:
$$\displaystyle e^{9 (t-2)} H(t-2)$$