Just wondering if someone could have a quick look over what I've done so far:

Assuming zero initial conditions, solve the following DE:

$\displaystyle \dot{x} + x = 2$

The Laplace Transform gives:

$\displaystyle sX(s) - x_0 + \frac{1}{s^2} = \frac{2}{s}$

Rearranging and using the fact that $\displaystyle x_0 =0$ gives us

$\displaystyle X(s) = \frac{2}{s^2} - \frac{1}{s^3}$

$\displaystyle X(s) = 2\frac{1!}{s^{1+1}} - \frac{1}{2} \frac{2!}{s^{2+1}}$

So $\displaystyle x(s) = 2t - \frac{t^2}{2}$?