code: def _nonlinear_2eq_order1_type2(x, y, t, eq):
      r"""
      Equations:
  
      .. math:: x' = e^{\lambda x} F(x,y)
  
      .. math:: y' = g(y) F(x,y)
  
      Solution:
  
      .. math:: x = \varphi(y), \int \frac{1}{g(y) F(\varphi(y),y)} \,dy = t + C_2
  
      where
  
      if `\lambda \neq 0`
  
      .. math:: \varphi = -\frac{1}{\lambda} log(C_1 - \lambda \int \frac{1}{g(y)} \,dy)
  
      if `\lambda = 0`
  
      .. math:: \varphi = C_1 + \int \frac{1}{g(y)} \,dy
  
      where `C_1` and `C_2` are arbitrary constants.
  
      """
      C1, C2 = get_numbered_constants(eq, num=2)
      n = Wild("n", exclude=[x(t), y(t)])
      f = Wild("f")
      u, v = symbols("u, v")
      r = eq[0].match(diff(x(t), t) - exp(n * x(t)) * f)
      g = ((diff(y(t), t) - eq[1]) / r[f]).subs(y(t), v)
      F = r[f].subs(x(t), u).subs(y(t), v)
      n = r[n]
      if n:
          phi = -1 / n * log(C1 - n * Integral(1 / g, v))
      else:
          phi = C1 + Integral(1 / g, v)
      phi = phi.doit()
      sol2 = solve(
          Integral(1 / (g * F.subs(u, phi)), v).doit() - t - C2, v
      )
      sol = []
      for sols in sol2:
          sol.append(Eq(x(t), phi.subs(v, sols)))
          sol.append(Eq(y(t), 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 34 for calling a global function with example usage: _nonlinear_2eq_order1_type2(x, y, t, eq) and returns: sol