code: def odesimp(ode, eq, func, hint):
      r"""
      Simplifies solutions of ODEs, including trying to solve for ``func`` and
      running :py:meth:`~sympy.solvers.ode.constantsimp`.
  
      It may use knowledge of the type of solution that the hint returns to
      apply additional simplifications.
  
      It also attempts to integrate any :py:class:`~sympy.integrals.integrals.Integral`\s
      in the expression, if the hint is not an ``_Integral`` hint.
  
      This function should have no effect on expressions returned by
      :py:meth:`~sympy.solvers.ode.dsolve`, as
      :py:meth:`~sympy.solvers.ode.dsolve` already calls
      :py:meth:`~sympy.solvers.ode.ode.odesimp`, but the individual hint functions
      do not call :py:meth:`~sympy.solvers.ode.ode.odesimp` (because the
      :py:meth:`~sympy.solvers.ode.dsolve` wrapper does).  Therefore, this
      function is designed for mainly internal use.
  
      Examples
      ========
  
      >>> from sympy import sin, symbols, dsolve, pprint, Function
      >>> from sympy.solvers.ode.ode import odesimp
      >>> x, u2, C1= symbols('x,u2,C1')
      >>> f = Function('f')
  
      >>> eq = dsolve(x*f(x).diff(x) - f(x) - x*sin(f(x)/x), f(x),
      ... hint='1st_homogeneous_coeff_subs_indep_div_dep_Integral',
      ... simplify=False)
      >>> pprint(eq, wrap_line=False)
                              x
                             ----
                             f(x)
                               /
                              |
                              |   /        1   \
                              |  -|u1 + -------|
                              |   |        /1 \|
                              |   |     sin|--||
                              |   \        \u1//
      log(f(x)) = log(C1) +   |  ---------------- d(u1)
                              |          2
                              |        u1
                              |
                             /
  
      >>> pprint(odesimp(eq, f(x), 1, {C1},
      ... hint='1st_homogeneous_coeff_subs_indep_div_dep'
      ... )) #doctest: +SKIP
          x
      --------- = C1
         /f(x)\
      tan|----|
         \2*x /
  
      """
      x = func.args[0]
      f = func.func
      C1 = get_numbered_constants(eq, num=1)
      constants = eq.free_symbols - ode.free_symbols
  
      # First, integrate if the hint allows it.
      eq = _handle_Integral(eq, func, hint)
      if hint.startswith("nth_linear_euler_eq_nonhomogeneous"):
          eq = simplify(eq)
      if not isinstance(eq, Equality):
          raise TypeError("eq should be an instance of Equality")
  
      # Second, clean up the arbitrary constants.
      # Right now, nth linear hints can put as many as 2*order constants in an
      # expression.  If that number grows with another hint, the third argument
      # here should be raised accordingly, or constantsimp() rewritten to handle
      # an arbitrary number of constants.
      eq = constantsimp(eq, constants)
  
      # Lastly, now that we have cleaned up the expression, try solving for func.
      # When CRootOf is implemented in solve(), we will want to return a CRootOf
      # every time instead of an Equality.
  
      # Get the f(x) on the left if possible.
      if eq.rhs == func and not eq.lhs.has(func):
          eq = [Eq(eq.rhs, eq.lhs)]
  
      # make sure we are working with lists of solutions in simplified form.
      if eq.lhs == func and not eq.rhs.has(func):
          # The solution is already solved
          eq = [eq]
  
      else:
          # The solution is not solved, so try to solve it
          try:
              floats = any(i.is_Float for i in eq.atoms(Number))
              eqsol = solve(
                  eq,
                  func,
                  force=True,
                  rational=False if floats else None,
              )
              if not eqsol:
                  raise NotImplementedError
          except (NotImplementedError, PolynomialError):
              eq = [eq]
          else:
  
              def _expand(expr):
                  numer, denom = expr.as_numer_denom()
  
                  if denom.is_Add:
                      return expr
                  else:
                      return powsimp(
                          expr.expand(), combine="exp", deep=True
                      )
  
              # XXX: the rest of odesimp() expects each ``t`` to be in a
              # specific normal form: rational expression with numerator
              # expanded, but with combined exponential functions (at
              # least in this setup all tests pass).
              eq = [Eq(f(x), _expand(t)) for t in eqsol]
  
          # special simplification of the lhs.
          if hint.startswith("1st_homogeneous_coeff"):
              for j, eqi in enumerate(eq):
                  newi = logcombine(eqi, force=True)
                  if isinstance(newi.lhs, log) and newi.rhs == 0:
                      newi = Eq(newi.lhs.args[0] / C1, C1)
                  eq[j] = newi
  
      # We cleaned up the constants before solving to help the solve engine with
      # a simpler expression, but the solved expression could have introduced
      # things like -C1, so rerun constantsimp() one last time before returning.
      for i, eqi in enumerate(eq):
          eq[i] = constantsimp(eqi, constants)
          eq[i] = constant_renumber(eq[i], ode.free_symbols)
  
      # If there is only 1 solution, return it;
      # otherwise return the list of solutions.
      if len(eq) == 1:
          eq = eq[0]
      return eq
  
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 13 for calling a global function with example usage: odesimp(ode, eq, func, hint) and returns: eq, expr, powsimp