This problem cannot be cleanly solved analytically (because f is discontinuous and obviously lacking a clean closed form), but is expressed by a beautiful and simple differential equation.
Huh, this is a great example. My historical relationship to differential equations has been mostly from the perspective of “it’s a method by which you eventually arrive at good analytic descriptions of systems”. I think this example really concretely illustrated why that’s a wrong perspective.
Huh, this is a great example. My historical relationship to differential equations has been mostly from the perspective of “it’s a method by which you eventually arrive at good analytic descriptions of systems”. I think this example really concretely illustrated why that’s a wrong perspective.