code: def sysode_linear_2eq_order1(match_):
      x = match_["func"][0].func
      y = match_["func"][1].func
      func = match_["func"]
      fc = match_["func_coeff"]
      eq = match_["eq"]
      r = {}
      t = list(list(eq[0].atoms(Derivative))[0].atoms(Symbol))[0]
      for i in range(2):
          eq[i] = Add(
              *[
                  terms / fc[i, func[i], 1]
                  for terms in Add.make_args(eq[i])
              ]
          )
  
      # for equations Eq(a1*diff(x(t),t), a*x(t) + b*y(t) + k1)
      # and Eq(a2*diff(x(t),t), c*x(t) + d*y(t) + k2)
      r["a"] = -fc[0, x(t), 0] / fc[0, x(t), 1]
      r["c"] = -fc[1, x(t), 0] / fc[1, y(t), 1]
      r["b"] = -fc[0, y(t), 0] / fc[0, x(t), 1]
      r["d"] = -fc[1, y(t), 0] / fc[1, y(t), 1]
      forcing = [S.Zero, S.Zero]
      for i in range(2):
          for j in Add.make_args(eq[i]):
              if not j.has(x(t), y(t)):
                  forcing[i] += j
      if not (forcing[0].has(t) or forcing[1].has(t)):
          r["k1"] = forcing[0]
          r["k2"] = forcing[1]
      else:
          raise NotImplementedError(
              "Only homogeneous problems are supported"
              + " (and constant inhomogeneity)"
          )
  
      if match_["type_of_equation"] == "type6":
          sol = _linear_2eq_order1_type6(x, y, t, r, eq)
      if match_["type_of_equation"] == "type7":
          sol = _linear_2eq_order1_type7(x, y, t, r, eq)
      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 29 for calling a global function with example usage: sysode_linear_2eq_order1(match_) and returns: sol