I am working on a project that uses numerical integration to solve some differential equations. Not coming from a solid math background, I have a problem understanding some integration methods. Specifically, I have the following equation:
$ \frac{d y}{d t} = \frac{u - y}{v} \,, $ where $u$ and $v$ are constants and $y(0)$ is known.
I solved this initially with a simple Euler integration and then with some other higher-order methods (Runge-Kutta 4). Then, I found another numerical integrator that did: $ y_{n+1} = y_{n} + (u - y_{n})(1 - e^{\frac{-\Delta t}{v}}) \,. $
My question is: what is this integration method? I checked and the results are basically the same, but I had no idea about this technique and I would like to know more about it.