Using Mathematica to Solve Differential Equations

Single differential equations

Systems of differential equations

You will notice that I use several different methods to solve systems of equations here.  This is partly because some of them (the sections on eigensystems and exponentiation of operators) are techniques covered in our text; I show you how to work those methods in Mathematica.  Honestly, however, most of the time you will probably use DSolve and NDSolve.  Be sure to read the first section on setting up systems in Mathematica, however.