code: def test_pde_classify():
      # When more number of hints are added, add tests for classifying here.
      f = Function("f")
      eq1 = a * f(x, y) + b * f(x, y).diff(x) + c * f(x, y).diff(y)
      eq2 = 3 * f(x, y) + 2 * f(x, y).diff(x) + f(x, y).diff(y)
      eq3 = a * f(x, y) + b * f(x, y).diff(x) + 2 * f(x, y).diff(y)
      eq4 = x * f(x, y) + f(x, y).diff(x) + 3 * f(x, y).diff(y)
      eq5 = (
          x**2 * f(x, y)
          + x * f(x, y).diff(x)
          + x * y * f(x, y).diff(y)
      )
      eq6 = y * x**2 * f(x, y) + y * f(x, y).diff(x) + f(x, y).diff(y)
      for eq in [eq1, eq2, eq3]:
          assert classify_pde(eq) == (
              "1st_linear_constant_coeff_homogeneous",
          )
      for eq in [eq4, eq5, eq6]:
          assert classify_pde(eq) == ("1st_linear_variable_coeff",)
  
file_path: sympy/sympy/solvers/tests/test_pde.py
imports: from sympy.core.function import Derivative, Function
  from sympy.core.relational import Eq
  from sympy.core.symbol import Symbol, symbols
  from sympy.functions.elementary.exponential import exp, log
  from sympy.functions.elementary.trigonometric import cos, sin
  from sympy.core import S
  from sympy.solvers.pde import pde_separate, pde_separate_add, pde_separate_mul, pdsolve, classify_pde, checkpdesol
  from sympy.testing.pytest import raises
label_desc: Use image node_id 5 for calling a global function with example usage: test_pde_classify() without return types