I actually asked a version of this question before, here: What is the formal, rigorous definition of a differential equation?. However, I should have asked what an equation is, first, which I did here: What is the formal definition of an equation?. But now that I have asked the question of what an equation is, and gotten a very detailed and rigorous answer, I want to revisit my original question. I want to know what is the formal and rigorous definition of a differential equation. I don't think it is simply a functional equation, like $f^2=f+1$. That is an equation involving real functions, but it is not a differential equation. So, then, what is the definition of differential equations?
2026-04-25 18:12:36.1777140756
An extremely rigorous and formal definition of differential equation.
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