code: def solve_ics(sols, funcs, constants, ics):
      """
      Solve for the constants given initial conditions
  
      ``sols`` is a list of solutions.
  
      ``funcs`` is a list of functions.
  
      ``constants`` is a list of constants.
  
      ``ics`` is the set of initial/boundary conditions for the differential
      equation. It should be given in the form of ``{f(x0): x1,
      f(x).diff(x).subs(x, x2):  x3}`` and so on.
  
      Returns a dictionary mapping constants to values.
      ``solution.subs(constants)`` will replace the constants in ``solution``.
  
      Example
      =======
      >>> # From dsolve(f(x).diff(x) - f(x), f(x))
      >>> from sympy import symbols, Eq, exp, Function
      >>> from sympy.solvers.ode.ode import solve_ics
      >>> f = Function('f')
      >>> x, C1 = symbols('x C1')
      >>> sols = [Eq(f(x), C1*exp(x))]
      >>> funcs = [f(x)]
      >>> constants = [C1]
      >>> ics = {f(0): 2}
      >>> solved_constants = solve_ics(sols, funcs, constants, ics)
      >>> solved_constants
      {C1: 2}
      >>> sols[0].subs(solved_constants)
      Eq(f(x), 2*exp(x))
  
      """
      # Assume ics are of the form f(x0): value or Subs(diff(f(x), x, n), (x,
      # x0)): value (currently checked by classify_ode). To solve, replace x
      # with x0, f(x0) with value, then solve for constants. For f^(n)(x0),
      # differentiate the solution n times, so that f^(n)(x) appears.
      x = funcs[0].args[0]
      diff_sols = []
      subs_sols = []
      diff_variables = set()
      for funcarg, value in ics.items():
          if isinstance(funcarg, AppliedUndef):
              x0 = funcarg.args[0]
              matching_func = [
                  f for f in funcs if f.func == funcarg.func
              ][0]
              S = sols
          elif isinstance(funcarg, (Subs, Derivative)):
              if isinstance(funcarg, Subs):
                  # Make sure it stays a subs. Otherwise subs below will produce
                  # a different looking term.
                  funcarg = funcarg.doit()
              if isinstance(funcarg, Subs):
                  deriv = funcarg.expr
                  x0 = funcarg.point[0]
                  variables = funcarg.expr.variables
                  matching_func = deriv
              elif isinstance(funcarg, Derivative):
                  deriv = funcarg
                  x0 = funcarg.variables[0]
                  variables = (x,) * len(funcarg.variables)
                  matching_func = deriv.subs(x0, x)
              for sol in sols:
                  if sol.has(deriv.expr.func):
                      diff_sols.append(
                          Eq(
                              sol.lhs.diff(*variables),
                              sol.rhs.diff(*variables),
                          )
                      )
              diff_variables.add(variables)
              S = diff_sols
          else:
              raise NotImplementedError(
                  "Unrecognized initial condition"
              )
  
          for sol in S:
              if sol.has(matching_func):
                  sol2 = sol
                  sol2 = sol2.subs(x, x0)
                  sol2 = sol2.subs(funcarg, value)
                  # This check is necessary because of issue #15724
                  if not isinstance(sol2, BooleanAtom) or not subs_sols:
                      subs_sols = [
                          s
                          for s in subs_sols
                          if not isinstance(s, BooleanAtom)
                      ]
                      subs_sols.append(sol2)
  
      # TODO: Use solveset here
      try:
          solved_constants = solve(subs_sols, constants, dict=True)
      except NotImplementedError:
          solved_constants = []
  
      # XXX: We can't differentiate between the solution not existing because of
      # invalid initial conditions, and not existing because solve is not smart
      # enough. If we could use solveset, this might be improvable, but for now,
      # we use NotImplementedError in this case.
      if not solved_constants:
          raise ValueError("Couldn't solve for initial conditions")
  
      if solved_constants == True:
          raise ValueError(
              "Initial conditions did not produce any solutions for constants. Perhaps they are degenerate."
          )
  
      if len(solved_constants) > 1:
          raise NotImplementedError(
              "Initial conditions produced too many solutions for constants"
          )
  
      return solved_constants[0]
  
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 5 for calling a global function with example usage: solve_ics(sols, funcs, constants, ics) and returns: solved_constants