Can you determine if a sympy expression has an explicit time dependence?

For example this example does have an explicit time dependence:

import sympy as sp
expr = sp.sympify("Add(Symbol('t'), Function('y')(Symbol('t')))")

But this example does not (even though t is a parameter of the y function.

import sympy as sp
expr = sp.sympify("Add(Integer(2), Function('y')(Symbol('t')))")