(maxima.info)Introduction to numerical solution of differential equations

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22.4 Introduction to numerical solution of differential equations
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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.