code: def test_euler_henonheiles():
      x = Function("x")
      y = Function("y")
      t = Symbol("t")
      L = sum(D(z(t), t) ** 2 / 2 - z(t) ** 2 / 2 for z in [x, y])
      L += -x(t) ** 2 * y(t) + y(t) ** 3 / 3
      assert euler(L, [x(t), y(t)], t) == [
          Eq(-2 * x(t) * y(t) - x(t) - D(x(t), t, t), 0),
          Eq(-x(t) ** 2 + y(t) ** 2 - y(t) - D(y(t), t, t), 0),
      ]
  
file_path: sympy/sympy/calculus/tests/test_euler.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.trigonometric import cos, sin
  from sympy.testing.pytest import raises
  from sympy.calculus.euler import euler_equations
label_desc: Use image node_id 3 for calling a global function with example usage: test_euler_henonheiles() without return types