Numerical Solutions to ODEs

Mathematica cannot find a direct solution to the following nonlinear ODE

NDSolve is a numerical method for finding a solution. An initial condition and the desired range of solution are required.

The results look kind of strange, perhaps, but they are a set of rules that provide a function that interpolates between values.   
    Here is how to find the approximate solution at three different values of x on the specified interval:

Created by Wolfram Mathematica 6.0  (13 November 2007)