these first 2 paragraphs are background to answer your question. i think they might be helpful, but if just confuse you then ignore 'em.
article III sec. 2 of const. says must be "arising under"
in osborne SC said that all this means that's constitutionally req. for fed ct. to hear a case is that federal matter be "an ingredient of original cause." that's very broad and would include most cases we study (e.g. mottley, merrel dow).
sec. 1331 of FRCP uses same lang. "arising under" but has been interpr. far more narrowly. so while constitutionally the legislature could allow fed. cts to hear any case where a federal matter is "an ingredient of original cause" the SC has said that based on sec 1331 of FRCP the legislature only granted federal cts ability to hear cases which fall into a smaller category.
there are two distinct views as to what fits under 1331 and thus fulfills the federal question jurisdiction that is required to try a case in federal ct.
1) in the P's suit the federal law must "create the cause of action." this is often referred to as the Holmes principle/test. under this test, we don't care if federal law authorizes you to sue, but rather, is federal law the cause of the action (shoshone mining). so for example, under this test, if you get into a car accident, if someone breaks a contract, or if there's an issue regarding a divorce, 99.9% (100%?) of the time the cause of action is a state matter. under this test, since the cause of action (accident/breach/divorce) is a state matter, the federal cts (aside from supreme ct if constitutional issue) were not granted power to hear the case by the legislature under 1331.
2) more commonly used today seems to be the mottley rule (even that has been expanded upon to some degree). here, a suit meets the federal question jurisdiction provided that the minimum neccessary to bring suit requires the P to prove a fed. law. we don't care that the P happened to raise a federal law in complaint to prove his case, nor do we care if P did or even had to raise a federal law to counter an argument by D. what we care is this: if the D said absolutely nothing, would the P absolutely need to prove a fed. law to win the case?
so now sometimes (though still very rarely) a car accident/breach of K/divorce might require the P to bring some fed. law to prove his case. even though the cause of action was a state matter, it still fits under sec. 1331 according to this 2nd test.
merrel dow brings up a diff. matter and since i dont even know if u still need this i'll leave that out for now. g'luck.