This tool uses 2 Data Tables to plot feature to plot 250 values of the functions a(x) and b(x) over the specified range. Similar to the 2nd order LODE solver tool, the 4th order Runge-Kutta method is used to calculate the first 3 values of the solution. and the Adams-Bashforth/Adams-Moulton method is used to get the rest of the solution. The computations are performed in columns U through AM.

For more details, see the page 2nd order LODE Solver: How it works

Do note that numerical methods have limitations and these must be kept in mind while using them or while interpreting the results obtained from them. Read this wiki page on numerical methods for an overview of numerical methods.