The problem statement, all variables and given/known data Now that I'm working it out as I'm typing it, I think I may have solved this problem; could still be a mistake though... This was an extra credit problem on the final for my into to diff eq class. I never saw anything like it before and I didn't finish it because I got stuck on one part. It's copied pretty much exactly as it was on the paper. Define [x] by  = 5  = 8  = 14 [-2] = -7 ... and [x]1 = [x] [x]2 = [[x]] [x]3 = [[[x]]] .... Solve dy/dx = x The attempt at a solution I see that [x] is basically the function f(x) = 3x - 1. Then I can find a formula for [x]1, [x]2, ... by plugging f(x) into itself and finding a pattern. [x]1 = 3x - 1 [x]2 = 9x - 4 [x]3 = 27x - 13 [x]4 = 81x - 40 ... Then I got [x]n = 3nx - (3n - 1)/2 Finding a closed form for the last term of the nth term of [x]n had me stuck and that was where I originally stopped on the problem. I used Wolframalpha to find a closed form, but is there a clever way of finding it just by looking at the numbers, without knowing the formula beforehand? I can't see it... Now if g(x) = x, then g(x) = 3x(10) - (3x - 1)/2 and I can integrate that to solve dy/dx = x. Correct? Something that kind of bothered me is that x looks like it can only be defined for natural numbers, so does dy/dx = x even make sense in the first place?