2nd Order ODEs

Once upon a time I was interested in Ordinary Differential Equations, so I was thinking ...
>That was your first mistake!

... I was thinking that I should solve one or two, numerically, just to ...
>What's that got to do with Investing stuff?

... just to entertain myself.

Here's a spreadsheet which I enjoy playing with:

To download, just click on the picture.

There's an explanation sheet which looks something like THIS
>You find this interesting?
If we solve:
dx/dt = x - x*y
dy/dt = -y + x*y
then it describes a rabbit population which tends to grow except when there are too many wolves in which case the rabbit population decreases and the wolves die off when there aren't many rabbits to eat so with fewer wolves the rabbits multiply and with lots of rabbits the wolf population grows again and ...

... and you can get pictures, sorta like so
which shows the rise and fall of the populations and ...

>Huh? There's just 2 rabbits, decreasing to 0.5 rabbits? You kidding?
Well, we can assume they're measured in hundreds ... or thousands or ...
How about another sheet which looks like THIS ??

Fixed Up

I ran across that old, old ODE spreadsheet described above and thought it was pretty crummy, so ...
>So you changed it.
Well ... yes. You used to have to modify a macro. Ugh!
Now you can just type in the equations and press a button and a Runge-Kutta integration scheme takes over.
It doesn''t matter. It solves and plots the solution
like this.

For a more simple-minded spreadsheet, you can try this one:

>Why simple-minded?
It don't do Runge-Kutta