How to divide by variable that belongs to y in Sympy
Since you are using SymPy, why not use its solver for such equations?
>>> from sympy import S, Function
>>> from sympy.abc import x
>>> f = Function('f')
>>> S('dydx-6*x*y*exp(y)').subs(y,f(x)).subs('dydx',f(x).diff(x))
-6*x*f(x)*exp(f(x)) + Derivative(f(x), x)
>>> dsolve(_)
Eq(Ei(exp_polar(I*pi)*f(x)), C1 + 3*x**2)
Else, if you have a product of factors and want those that contain a certain symbol you can just use as_independent to separate them:
>>> nony, withy = (x*y*exp(y)).as_independent(y); (nony, withy)
(x, y*exp(y))