### 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.

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