I had the differential equation $y'+y=\frac1x$, which I solved for $y$ as a power series:
Which was a power series at $\infty$, so it doesn't really help me much.
So my first question is whether or not $y$ is solvable here (as a power series if needed) where it actually converges.
My second question is if it pure coincidence that the summation is very similar to the power series of $e^x$.
Is there some reason for their very similar forms, or just my stumbling upon these two unrelated power series?