Show HN: Differential Equations Explained
> Some of them don't even really have solutions (non-linear differential equations).There certainly are differential equations without solutions, but I'm almost positive that's not what's meant here.  Rather, it is very likely that one can't find an explicit solution to a non-linear equation (EDIT: although there are non-linear equations that one can solve, such as $\dot y = 1/y$, whose solutions have graphs lying on straight lines through the origin); but there is a huge difference between an equation that doesn't have a solution and one whose solution we can't find.For example, away from singularities, one can approximate the solution of a differential equation, even a non-linear one, numerically to an arbitrarily high degree of accuracy, almost exactly as the author does for linear equations.EDIT:  TheLoneWolfling (https://news.ycombinator.com/item?id=9654767 )'s point that this numerical simulation can get hard very quickly is well taken, and probably more important in applications than abstract existence results.  Non-linear equations really are hard!