code: def test_intcurve_diffequ():
      t = symbols("t")
      start_point = R2_r.point([1, 0])
      vector_field = -R2.y * R2.e_x + R2.x * R2.e_y
      equations, init_cond = intcurve_diffequ(
          vector_field, t, start_point
      )
      assert (
          str(equations)
          == "[f_1(t) + Derivative(f_0(t), t), -f_0(t) + Derivative(f_1(t), t)]"
      )
      assert str(init_cond) == "[f_0(0) - 1, f_1(0)]"
      equations, init_cond = intcurve_diffequ(
          vector_field, t, start_point, R2_p
      )
      assert (
          str(equations)
          == "[Derivative(f_0(t), t), Derivative(f_1(t), t) - 1]"
      )
      assert str(init_cond) == "[f_0(0) - 1, f_1(0)]"
  
imports: from sympy.core import Lambda, Symbol, symbols
  from sympy.diffgeom.rn import R2, R2_p, R2_r, R3_r, R3_c, R3_s, R2_origin
  from sympy.diffgeom import Manifold, Patch, CoordSystem, Commutator, Differential, TensorProduct, WedgeProduct, BaseCovarDerivativeOp, CovarDerivativeOp, LieDerivative, covariant_order, contravariant_order, twoform_to_matrix, metric_to_Christoffel_1st, metric_to_Christoffel_2nd, metric_to_Riemann_components, metric_to_Ricci_components, intcurve_diffequ, intcurve_series
  from sympy.simplify import trigsimp, simplify
  from sympy.functions import sqrt, atan2, sin
  from sympy.matrices import Matrix
  from sympy.testing.pytest import raises, nocache_fail
  from sympy.testing.pytest import warns_deprecated_sympy
label_desc: Use image node_id 11 for calling a global function with example usage: test_intcurve_diffequ() without return types