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Complete this python program:
def _undetermined_coefficients_match(expr, x):
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#Here is the Python code you requested.

    """Returns a trial function match if undetermined coefficients can be applied
    to ``expr``, and ``None`` otherwise.
    A trial expression can be found for an expression for use with the method
    of undetermined coefficients if the expression is an
    additive/multiplicative combination of constants, polynomials in `x` (the
    independent variable of expr), `\sin(a x + b)`, `\cos(a x + b)`, and
    `e^{a x}` terms (in other words, it has a finite number of linearly
    independent derivatives).
    Note that you may still need to multiply each term returned here by
    sufficient `x` to make it linearly independent with the solutions to the
    homogeneous equation.
    This is intended for internal use by ``undetermined_coefficients`` hints.
    SymPy currently has no way to convert `\sin^n(x) \cos^m(y)` into a sum of
    only `\sin(a x)` and `\cos(b x)` terms, so these are not implemented.  So,
    for example, you will need to manually convert `\sin^2(x)` into `[1 +
    \cos(2 x)]/2` to properly apply the method of undetermined coefficients on
    it.
    Examples
    >>> from sympy import log, exp
    >>> from sympy.solvers.ode import _undetermined_coefficients_match
    >>> from sympy.abc import x
    >>> _undetermined_coefficients_match(9*x*exp(x) + exp(-x), x)
    {\test\: True, \trialset\: {x*exp(x), exp(-x), exp(x)}}
    >>> _undetermined_coefficients_match(log(x), x)
    {\test\: False}
    """
    a = Wild('a', exclude=[x])
    b = Wild('b', exclude=[x])
    expr = powsimp(expr, combine='exp')
    retdict = {}
    def _test_term(expr, x):
        '\n                                Test    if    ``expr``    fits    the    proper    form    for    undetermined    coefficients.\n                                '
        if expr.is_Add:
            return all((_test_term(i, x) for i in expr.args))
        elif expr.is_Mul:
            if expr.has(sin, cos):
                foundtrig = False
                for i in expr.args:
                    if i.has(sin, cos):
                        if foundtrig:
                            return False
                        else:
                            foundtrig = True
            return all((_test_term(i, x) for i in expr.args))
        elif expr.is_Function:
            if (expr.func in (sin, cos, exp)):
                if expr.args[0].match(((a * x) + b)):
                    return True
                else:
                    return False
            else:
                return False
        elif (expr.is_Pow and expr.base.is_Symbol and expr.exp.is_Integer and (expr.exp >= 0)):
            return True
        elif (expr.is_Pow and expr.base.is_number):
            if expr.exp.match(((a * x) + b)):
                return True
            else:
                return False
        elif (expr.is_Symbol or expr.is_number):
            return True
        else:
            return False
    def _get_trial_set(expr, x, exprs=set([])):
        '\n                                Returns    a    set    of    trial    terms    for    undetermined    coefficients.\n\n                                The    idea    behind    undetermined    coefficients    is    that    the    terms    expression\n                                repeat    themselves    after    a    finite    number    of    derivatives,    except    for    the\n                                coefficients    (they    are    linearly    dependent).        So    if    we    collect    these,\n   ...