How to select dependent variables from pde system?

Question

Let's say I have a following pde:

pde = x^2 u[x, y] D[u[x, y], {x}] + v[x, y] D[u[x, y], {y}]

I want select the dependent variables:

desiredResult = {u[x, y], D[u[x, y], {x}], v[x, y], D[u[x, y], {y}] }

I have tried many things and best result is this one:

depVars = {u, v}.
DeleteDuplicates@Flatten[Cases[pde,
 Derivative[___][#1][___] | #2[___]] & @@@ Subsets[depVars, {2}], 1]

But it works only for those ones, where dependent variables aren't multiplied with some expression. Is there any way to extract all the dependent variables?

Answer 1

How about this?

DeleteDuplicates@
  Cases[pde, Derivative[___][#1][___] | #1[___], Infinity] &@
   (Alternatives @@ depVars)