A derivation on a polynomial ring $K[x,y]$ is said to be integrable if there exists a second derivation that commutes with it and is $K[x,y]$-independent of it. If a derivation is integrable, then the data provided by the second derivation can be used to solve the corresponding differential equation. We present recent results on integrability.
This is joint work with Joel Nagloo and Alexey Ovchinnikov.