I'm struggling with an exercise in Arnold's book about DEs, maybe someone could suggest a hint on how to solve it?
An exercise goes like this:
find the group of symmetries for a vector field $x\partial_x+y\partial_y$ on a plane with coordinates $(x,y).$ I know that rotations and homothetic transformations cenetred at the origin.
I was unable to prove that all symmetries are linear (i.e. generated by homotheties and rotation). I wrote down a system of PDEs to give conditions on diffeomorphism to preserve vector field, however, I don't know how to solve it.