We know that in characteristic $0$, all algebraic series are differentiably finite.
Is this true in positive characteristic? I look at the [proof](https://www.e-periodica.ch/cntmng?pid=ens-001:1964:10::61), indeed we need to the
characteristic to be $0$ for the proof to work.
If it is not true in positive characteristic, is there a counter-example?


Thank you in advance!



Are algebraic power series in positive characteristics D-finite?
Over a field of characteristic $p$, the $p$-th derivative of any power series is $0$, and so every power series over a field of finite characteristic is $D$-finite.


