22.5 Introduction to numerical solution of differential equations

The Ordinary Differential Equations (ODE) solved by the functions in this section should have the form,

       dy
       -- = F(x,y)
       dx

which is a first-order ODE. Higher order differential equations of order n must be written as a system of n first-order equations of that kind. For instance, a second-order ODE should be written as a system of two equations

       dx               dy
       -- = G(x,y,t)    -- = F(x,y,t) 
       dt               dt

The first argument in the functions will be a list with the expressions on the right-side of the ODE’s. The variables whose derivatives are represented by those expressions should be given in a second list. In the case above those variables are x and y. The independent variable, t in the examples above, might be given in a separated option. If the expressions given do not depend on that independent variable, the system is called autonomous.