code: def _nonlinear_2eq_order1_type3(x, y, t, eq):
      r"""
      Autonomous system of general form
  
      .. math:: x' = F(x,y)
  
      .. math:: y' = G(x,y)
  
      Assuming `y = y(x, C_1)` where `C_1` is an arbitrary constant is the general
      solution of the first-order equation
  
      .. math:: F(x,y) y'_x = G(x,y)
  
      Then the general solution of the original system of equations has the form
  
      .. math:: \int \frac{1}{F(x,y(x,C_1))} \,dx = t + C_1
  
      """
      C1, C2, C3, C4 = get_numbered_constants(eq, num=4)
      v = Function("v")
      u = Symbol("u")
      f = Wild("f")
      g = Wild("g")
      r1 = eq[0].match(diff(x(t), t) - f)
      r2 = eq[1].match(diff(y(t), t) - g)
      F = r1[f].subs(x(t), u).subs(y(t), v(u))
      G = r2[g].subs(x(t), u).subs(y(t), v(u))
      sol2r = dsolve(Eq(diff(v(u), u), G / F))
      if isinstance(sol2r, Equality):
          sol2r = [sol2r]
      for sol2s in sol2r:
          sol1 = solve(
              Integral(1 / F.subs(v(u), sol2s.rhs), u).doit() - t - C2,
              u,
          )
      sol = []
      for sols in sol1:
          sol.append(Eq(x(t), sols))
          sol.append(Eq(y(t), (sol2s.rhs).subs(u, sols)))
      return sol
  
imports: from sympy.core import Add, S, Mul, Pow, oo
  from sympy.core.containers import Tuple
  from sympy.core.expr import AtomicExpr, Expr
  from sympy.core.function import Function, Derivative, AppliedUndef, diff, expand, expand_mul, Subs
  from sympy.core.multidimensional import vectorize
  from sympy.core.numbers import nan, zoo, Number
  from sympy.core.relational import Equality, Eq
  from sympy.core.sorting import default_sort_key, ordered
  from sympy.core.symbol import Symbol, Wild, Dummy, symbols
  from sympy.core.sympify import sympify
  from sympy.core.traversal import preorder_traversal
  from sympy.logic.boolalg import BooleanAtom, BooleanTrue, BooleanFalse
  from sympy.functions import exp, log, sqrt
  from sympy.functions.combinatorial.factorials import factorial
  from sympy.integrals.integrals import Integral
  from sympy.polys import Poly, terms_gcd, PolynomialError, lcm
  from sympy.polys.polytools import cancel
  from sympy.series import Order
  from sympy.series.series import series
  from sympy.simplify import collect, logcombine, powsimp, separatevars, simplify, cse
  from sympy.simplify.radsimp import collect_const
  from sympy.solvers import checksol, solve
  from sympy.utilities import numbered_symbols
  from sympy.utilities.iterables import uniq, sift, iterable
  from sympy.solvers.deutils import _preprocess, ode_order, _desolve
  from .single import SingleODEProblem, SingleODESolver, solver_map
label_desc: Use image node_id 35 for calling a global function with example usage: _nonlinear_2eq_order1_type3(x, y, t, eq) and returns: sol