From owner-help-octave at bevo dot che dot wisc dot edu  Fri Dec  1 11:43:56 1995
Subject: Re: can i do ODE2 problems with lsode ?
From: przemek at rrdjazz dot nist dot gov (Przemek Klosowski)
To: help-octave at bevo dot che dot wisc dot edu, spaz@u.washington.edu
Date: Fri, 01 Dec 1995 12:39:58 -0500

	   Here is the function that i want to try and solve first, since i
   think it is a "simple" example of what comes in the real stuff.

	   d^2 x                       dx
	   ----- + lambda*( x^2 - 1 )* -- + x = 0
	   dt^2                        dt

   my problem is that this is a 2nd order eq and lsode looks like it only
   wants 1rst order eq's.

	   Now, i *thought* that any nOrder ode can be represented as an
   Nsystem of 1rst order diffeq's.

It is fairly trivial, and I am sure it must be covered somewhere in these
texts: you simply introduce a pseudo-independent variable y = dx/dt
and reformulate your equations as

	    d  ( x )     (            y           )
	   --  (   )  =  (                        )
	   dt  ( y )     ( lambda * (x^2-1)*y + x )

(a 2-D non-linear first-order equation).