I would say the assumption is that people heading to mathematics graduate school know about the Wronskian, but this assumption isn't universally true.
Certainly, anyone who has studied a semester of differential equations (and is heading to graduate school) should know it.
However, there is a substantial minority of people interested in pure mathematics of a generally algebraic bent who never study differential equations. (I was one of these people until I was assigned to teach it!)
There really isn't anything that's universally expected (rather than merely generally assumed) of people heading to mathematics graduate school other than an ability to read and write proofs, and some folks doing mathematical modelling might even disagree with that.