dsolve should not preprocess ODEs

[oscarbenjamin]

CC @Mohitbalwani26

The ODE below should be easy for dsolve to solve using the nth_algebraic hint. It doesn't work though because dsolve preprocesses the ODE and evaluates all the derivatives so the nth_algebraic solver doesn't get to see the unevaluated derivative form that it knows how to solve. Although classify_ode says nth_algebraic can solve it dsolve will not use the nth_algebraic hint and then an exception is raised in the series solvers. The preprocessing in dsolve should be removed so that nth_algebraic can access the ODE in its original unprocessed form.

In [1]: eq = Derivative(f(x)*g(x), (x, 2))

In [2]: eq
Out[2]: 
  2           
 d            
───(f(x)⋅g(x))
  2           
dx            

In [3]: classify_ode(eq, f(x))
Out[3]: ('nth_algebraic', '2nd_power_series_ordinary', 'nth_algebraic_Integral')

In [4]: dsolve(eq, f(x))
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-4-3a286ce8891f> in <module>
----> 1 dsolve(eq, f(x))

~/current/sympy/sympy/sympy/solvers/ode/ode.py in dsolve(eq, func, hint, simplify, ics, xi, eta, x0, n, **kwargs)
    637             # The key 'hint' stores the hint needed to be solved for.
    638             hint = hints['hint']
--> 639             return _helper_simplify(eq, hint, hints, simplify, ics=ics)
    640 
    641 def _helper_simplify(eq, hint, match, simplify=True, ics=None, **kwargs):

~/current/sympy/sympy/sympy/solvers/ode/ode.py in _helper_simplify(eq, hint, match, simplify, ics, **kwargs)
    668             sols = solvefunc.get_general_solution()
    669         else:
--> 670             sols = solvefunc(eq, func, order, match)
    671         if iterable(sols):
    672             rv = [odesimp(eq, s, func, hint) for s in sols]

~/current/sympy/sympy/sympy/solvers/ode/ode.py in ode_2nd_power_series_ordinary(eq, func, order, match)
   2391     # Finding the recurrence relation in terms of the largest term.
   2392     fargs = req.atoms(AppliedUndef)
-> 2393     maxf = max(fargs, key = lambda x: x.args[0])
   2394     minf = min(fargs, key = lambda x: x.args[0])
   2395     if minf.args[0].is_Symbol:

~/current/sympy/sympy/sympy/core/relational.py in __bool__(self)
    396 
    397     def __bool__(self):
--> 398         raise TypeError("cannot determine truth value of Relational")
    399 
    400     def _eval_as_set(self):

TypeError: cannot determine truth value of Relational

There also seems to be a bug here in the 2nd_power_series_ordinary solver.