Results (Multiplication and Division Properties)

Q. The inverse Laplace transform of $F\left(s\right)=\frac{s+3}{s^2+2s+1}$ for $t\ge 0$ is

1. $e^{-t}+3t{e}^{-t}$
2. $e^{-t}+4t{e}^{-t}$
3. $e^{-t}+2t{e}^{-t}$
4. $3t{e}^{-t}$

Q. A solution for the differential equation $\dot{x}\left(t\right)+2x\left(t\right)=\delta \left(t\right)$ with initial condition x(0) = 0 is

1. $e^{-2t}u\left(t\right)$
2. $e^{-2t}u\left(t\right)$
3. $e^{-2t}u\left(t\right)$
4. $e^{t}u\left(t\right)$