How can you define the difference between for example Math and Philosophy and Sociology or Biology. What makes a philosophical question a philosophical question. Is this clearly defined?
One long-standing answer to this question is that philosophy asks "why" questions, whereas scientists ask "how" questions (see Socrates' remarks to that effect in the Phaedo).
There is a proper sub-discipline of philosophy called metaphilosophy, which takes this question seriously and in its many journals presents the thoughts of giants ancient (Plato, Aristotle, David, other Greeks, Arabs, Persians) as well as contemporary (e.g. Rescher, Hansson, Floridi, and many others). For a balanced treatment of this question I would suggest that you do some googling of the term.
From a Carnapian Point of View
A position that I find attractive has been put forth by Carnap and several other logical empiricists:
Thesis: Philosophy is the logic of science.
I'll quote from his essay "On the Character of Philosophic Problems" (1984), which begins as follows:
"Philosophers have ever declared that their problems lie at a different level from the problems of the empirical sciences. Perhaps one may agree with this assertion; the question is, however, where should one seek this level." (p. 5)
He next criticizes metaphysics and ethics for attempting to posit this level "behind the objects of empirical science", for wishing "to enquire after the essence, the ultimate cause of things." This is not something I agree with, but it provides some contrast for what he says next:
"In order to discover the correct standpoint of the philosopher, which differs from that of the empirical investigator, we must not penetrate behind the objects of empirical science into the presumably some kind of transcendent level; on the contrary we must take a step back and take science itself as the object. Philosophy is the theory of science." (p. 6)
He immediately adds that 'science' he uses "in the comprehensive sense of the collective system of the knowledge of any kind of entity; physical and psychic, natural and social entities." Next comes the explanation for the initial thesis. He begins by saying what sort of a theory philosophy is not:
"One may consider science from various viewpoints; e.g. whether one can institute a psychological investigation considering the activities of observation, deduction, formulation of theories, etc., or sociological investigations concerning the economical and cultural conditions of the pursuit of science. These provinces—although most important—are not meant here. Psychology and sociology are empirical sciences; they do not belong to philosophy even though they are often pursued by the same person, and have torn loose from philosophy as independent branches of science only in our own times." (p. 6)
Next he states his positive thesis (labeled 'Thesis' above):
"Philosophy deals with science only from the logical viewpoint. Philosophy is the logic of science, i.e., the logical analysis of the concepts, propositions, proofs, theories of science, as well as of those which we select in available science as common to the possible methods of constructing concepts, proofs, hypotheses, theories." (p. 6)
Lastly, in his characteristic undogmatic style Carnap concludes the section with the following:
"With this thesis the question as to the character of philosophic problems is not by any means already solved. Very much comes into question right at this point. We should consequently ask here: what character, what logical nature, do the questions and answers of the logic of science have? For those who are with us in the conception that philosophy is the logic of science the question of the character of philosophic problems will be answered thereby as well." (pp. 6-7)
This is, as I stated at the beginning of my post, simply one view I personally find attractive. It's not an uncontroversial position, but I think if one is able to postpone immediate disagreement upon reading the remarks on metaphysics and ethics, one may come to find the view quite attractive.
One problem with answering this is that prominent philosophers, past and present, have offered inconsistent answers. Rudolf Carnap's definition for instance, described in an answer here by Hunan Rostoyman, is of historical interest, and may be attractive, but fails to reflect a lot of work that's widely agreed to be squarely philosophy.
A way of describing the limits of Philosophy that I think better captures its current and past boundaries is that philosophical questions are questions of general interest which cannot be resolved empirically. I mean, they cannot be resolved scientifically or by observation.
A reason to limit Philosophy this way is that Philosophy has historically worked on a large number of questions which eventually shifted into the realm of Natural Philosophy, or later, "science," as our ability to answer them empirically improved. The nature of time, the nature and reality of matter, the nature of atoms, the origins of human beings, and similar questions were philosophical questions for a long time, in that philosophers could offer arguments for and against the coherence of some understandings of them, but could not answer them scientifically. As science improved, those questions in large part moved out of philosophy, and only some philosophical aspects of them remained. Philosophers of physics still work on questions about time that go beyond what science says, for instance. Some questions, like what is the best life for a human being, or whether it's ever wrong to lie, will (I suggest) never be answered empirically, to any degree.
One fairly minor, but growing, exception to this in contemporary philosophy is Experimental Philosophy, or X-Phi. But I would suggest understanding that movement as social science applied to informing our understanding of (as opposed to philosophically answering) certain philosophical questions that are amenable to it.
I think there is a lot of truth to what iphigenie has said in the comments about it being a library label. There are philosophical questions addressed in all of the sciences and scientific topics are found in philosophy.
But because of the way academia works, the gap is a bit wider than this might suggest. Philosophers end up reading work by philosophers, physicists primarily read work by other physicists, biologists: other biologists and so on. This in turn affects the language used, the impact of ideas, and reduces the cross talk between them. This is before we start on the various prejudices that this breeds. I imagine that if one drew a graph of citations, one would find a fairly strong grouping of different subjects.
So, I would say that there is a fairly strong boundary between the academic disciplines, each discipline gets it's own independent "momentum", affecting which questions are being asked, and how they are framed and addressed.
You might say this is just the structure of academia and completely misses the point about whether a question is philosophical or not.
But I don't think it's irrelevant. I'd like to illustrate this with a case from biology, the question "what is an organism?" - is this a philosophical question?
If you looked at what I would consider the philosophical side of the biology literature you would find rather empirical approaches. The authors of this paper draws from empirical approaches, and they end up focusing primarily on cooperation and adaptation - all in the tradition of evolutionary biology. The aim, it seems, is to understand evolution.
But if you look at what I would consider the biological side of philosophy literature (for example, these), there are completely different approaches, concerning autonomy and agency. Concepts follow in a vaguely continental philosophical tradition. The aim being a general understanding of the general questions concerning life.
So, there are more empirical and more philosophical answers to the same question. I would suggest that a better distinction would be between philosophical or non-philosophical traditions, how different groups of people have decided to address the same salient questions.