code: def constantsimp(expr, constants):
      r"""
      Simplifies an expression with arbitrary constants in it.
  
      This function is written specifically to work with
      :py:meth:`~sympy.solvers.ode.dsolve`, and is not intended for general use.
  
      Simplification is done by "absorbing" the arbitrary constants into other
      arbitrary constants, numbers, and symbols that they are not independent
      of.
  
      The symbols must all have the same name with numbers after it, for
      example, ``C1``, ``C2``, ``C3``.  The ``symbolname`` here would be
      '``C``', the ``startnumber`` would be 1, and the ``endnumber`` would be 3.
      If the arbitrary constants are independent of the variable ``x``, then the
      independent symbol would be ``x``.  There is no need to specify the
      dependent function, such as ``f(x)``, because it already has the
      independent symbol, ``x``, in it.
  
      Because terms are "absorbed" into arbitrary constants and because
      constants are renumbered after simplifying, the arbitrary constants in
      expr are not necessarily equal to the ones of the same name in the
      returned result.
  
      If two or more arbitrary constants are added, multiplied, or raised to the
      power of each other, they are first absorbed together into a single
      arbitrary constant.  Then the new constant is combined into other terms if
      necessary.
  
      Absorption of constants is done with limited assistance:
  
      1. terms of :py:class:`~sympy.core.add.Add`\s are collected to try join
         constants so `e^x (C_1 \cos(x) + C_2 \cos(x))` will simplify to `e^x
         C_1 \cos(x)`;
  
      2. powers with exponents that are :py:class:`~sympy.core.add.Add`\s are
         expanded so `e^{C_1 + x}` will be simplified to `C_1 e^x`.
  
      Use :py:meth:`~sympy.solvers.ode.ode.constant_renumber` to renumber constants
      after simplification or else arbitrary numbers on constants may appear,
      e.g. `C_1 + C_3 x`.
  
      In rare cases, a single constant can be "simplified" into two constants.
      Every differential equation solution should have as many arbitrary
      constants as the order of the differential equation.  The result here will
      be technically correct, but it may, for example, have `C_1` and `C_2` in
      an expression, when `C_1` is actually equal to `C_2`.  Use your discretion
      in such situations, and also take advantage of the ability to use hints in
      :py:meth:`~sympy.solvers.ode.dsolve`.
  
      Examples
      ========
  
      >>> from sympy import symbols
      >>> from sympy.solvers.ode.ode import constantsimp
      >>> C1, C2, C3, x, y = symbols('C1, C2, C3, x, y')
      >>> constantsimp(2*C1*x, {C1, C2, C3})
      C1*x
      >>> constantsimp(C1 + 2 + x, {C1, C2, C3})
      C1 + x
      >>> constantsimp(C1*C2 + 2 + C2 + C3*x, {C1, C2, C3})
      C1 + C3*x
  
      """
      # This function works recursively.  The idea is that, for Mul,
      # Add, Pow, and Function, if the class has a constant in it, then
      # we can simplify it, which we do by recursing down and
      # simplifying up.  Otherwise, we can skip that part of the
      # expression.
  
      Cs = constants
  
      orig_expr = expr
  
      constant_subexprs = _get_constant_subexpressions(expr, Cs)
      for xe in constant_subexprs:
          xes = list(xe.free_symbols)
          if not xes:
              continue
          if all(expr.count(c) == xe.count(c) for c in xes):
              xes.sort(key=str)
              expr = expr.subs(xe, xes[0])
  
      # try to perform common sub-expression elimination of constant terms
      try:
          commons, rexpr = cse(expr)
          commons.reverse()
          rexpr = rexpr[0]
          for s in commons:
              cs = list(s[1].atoms(Symbol))
              if (
                  len(cs) == 1
                  and cs[0] in Cs
                  and cs[0] not in rexpr.atoms(Symbol)
                  and not any(cs[0] in ex for ex in commons if ex != s)
              ):
                  rexpr = rexpr.subs(s[0], cs[0])
              else:
                  rexpr = rexpr.subs(*s)
          expr = rexpr
      except IndexError:
          pass
      expr = __remove_linear_redundancies(expr, Cs)
  
      def _conditional_term_factoring(expr):
          new_expr = terms_gcd(
              expr, clear=False, deep=True, expand=False
          )
  
          # we do not want to factor exponentials, so handle this separately
          if new_expr.is_Mul:
              infac = False
              asfac = False
              for m in new_expr.args:
                  if isinstance(m, exp):
                      asfac = True
                  elif m.is_Add:
                      infac = any(
                          isinstance(fi, exp)
                          for t in m.args
                          for fi in Mul.make_args(t)
                      )
                  if asfac and infac:
                      new_expr = expr
                      break
          return new_expr
  
      expr = _conditional_term_factoring(expr)
  
      # call recursively if more simplification is possible
      if orig_expr != expr:
          return constantsimp(expr, Cs)
      return expr
  
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 18 for calling a global function with example usage: constantsimp(expr, constants) and returns: expr, new_expr, constantsimp