"Whatever was born, must die."
That sounds like a self-evident truth to me, heartless though it might be to illustrate it with a photo of cute newborn puppies.
Let's call our above statement T. Let's also observe at once that in contrast to many of the propositions that are bruited about as self-evident truths, it can't plausibly be considered a tautology.
T, above, is very different from, say, "a triangle has three lines." The latter can be understood as meaning, "that which we call a 'triangle' has three lines" so the question of a possible exception doesn't arise.
T doesn't read like "that which we say has been 'born' must die."
I make a ponderous point of this because the synthetic/analytic distinction has come under heavy criticism in philosophical circles for decades now. If I recall correctly, Quine -- who is number 1 on the list I posted here yesterday -- made his reputation with an essay on the subject. So we can't simply use those terms innocently any longer. But however one wants to say it, T is a proposition very different from our statement about triangles, yet equally plausible as an exceptionless truth.