Mathematica will also permit numerical solutions to a given differential equation. In contrast to the limited discussion of numerical solutions presented here, the scheme that Mathematica uses dynamically determines the (now variable length) step size as it performs the computation. Default components of the numerical solution such as accuracy and maximum step size are used by Mathematica unless overridden by the user. One of the Mathematica functions used to produce a numerical solution is NDSolve, which is a natural counterpart to the DSolve method introduced in example 5.11. The NDSolve function of Mathematica is illustrated below.
