human
Here's a good function header given the following:
I wrote the below code

    def _sympify(eq):
        return list(map(sympify, (eq if iterable(eq) else [eq])))
    eqs = _sympify(eqs)
    for i in range(len(eqs)):
        if isinstance(eqs[i], Equality):
            eqs[i] = (eqs[i].lhs - eqs[i].rhs)
    if (func is None):
        funcs = []
        for eq in eqs:
            derivs = eq.atoms(Derivative)
            func = set().union(*[d.atoms(AppliedUndef) for d in derivs])
            for func_ in func:
                funcs.append(func_)
        funcs = list(set(funcs))
    if ((not all(((isinstance(func, AppliedUndef) and (len(func.args) == 1)) for func in funcs))) and (len({func.args for func in funcs}) != 1)):
        raise ValueError(('func    must    be    a    function    of    one    variable,    not    %s' % func))
    for sol in sols:
        if (len(sol.atoms(AppliedUndef)) != 1):
            raise ValueError('solutions    should    have    one    function    only')
    if (len(funcs) != len({sol.lhs for sol in sols})):
        raise ValueError('number    of    solutions    provided    does    not    match    the    number    of    equations')
    t = funcs[0].args[0]
    dictsol = dict()
    for sol in sols:
        func = list(sol.atoms(AppliedUndef))[0]
        if (sol.rhs == func):
            sol = sol.reversed
        solved = ((sol.lhs == func) and (not sol.rhs.has(func)))
        if (not solved):
            rhs = solve(sol, func)
            if (not rhs):
                raise NotImplementedError
        else:
            rhs = sol.rhs
        dictsol[func] = rhs
    checkeq = []
    for eq in eqs:
        for func in funcs:
            eq = sub_func_doit(eq, func, dictsol[func])
        ss = simplify(eq)
        if (ss != 0):
            eq = ss.expand(force=True)
        else:
            eq = 0
        checkeq.append(eq)
    if ((len(set(checkeq)) == 1) and (list(set(checkeq))[0] == 0)):
        return (True, checkeq)
    else:
        return (False, checkeq)

What's a good function header?
assistant
#Here's a good function header.

def checksysodesol(eqs, sols, func=None):