The problem is as follows:

$\displaystyle \frac{d}{dt}x(t) = x(t-1)$ with $\displaystyle x(t) = 1$ for $\displaystyle t \in [-1,0]$.

The solution is given by $\displaystyle x(t) = \sum_{k = 0}^{n} \frac{t-(k-1))^k}{k!}$ for $\displaystyle n-1 \leq t \leq n$.

Find the solution using the method of steps.

I have no idea what the method of steps is and I can't seem to find anything about it online. Any help/hints would be much appreciated!