Sheilah's got a good point. I was thinking that might be a problem, but forgot the proper way to specificy things so it would be correctly understood.
Meantime, I've stumbled on to a most interesting site...
http://www.exampleproblems.com Just like the URL says, it has example problems in a bunch of different mathmatical subjects. I found it while looking for a good juicy partial differential equation, but I'm thinking now that something like that may be more trouble than it's worth (as, come to think, PDEs in general tend to be...).
What's interesting, though, is that there's a link off to the left (under "navigation") which takes you to a random page on the site. It's kind of funny. If you keep clicking it, you can get a simple and direct trig problem followed by some basic algebra and then find yourself staring at a jumble of multiple equations with differentials all over the place and Fourier transforms...
*click, click*
Ooo,
here 's one of those things I was talking about that look so darned simple until you start trying to solve them... Take a look at what you're starting with, then scroll down to see the "solution."
*click, click*
Oh,
this might work...
You'd read it as:
"If Y double prime plus four Y prime plus three Y equals zero, with initial conditions of Y equals one and Y prime equals zero, then Y as a function of t would be...
"Let's see... Roots of negative one and negative three... So the general solution would be of the form C One times e to the negative t plus C Two times E to the negative three t... Plug in the initial conditions... C One equals one minus C Two and... negative C One minus negative thee C Two equals zero... Sub in the first equation... Negative one plus C Two minus three C Two equals zero, so C Two equals negative one half, which means C One equals one plus a half, which is three halves. So... Y as a function of t would be...
"Three halves e to the negative t minus one half e to the negative three t. Simple."
You could, of course, drop the middle paragraph to avoid making your readers' eyes cross. You could also change "Y double prime" to "the second derivative of Y" and "Y prime" to "the first derivative of Y." You might also specify the initial conditions as "Y of zero" and "Y prime of zero" or "Y at time zero" or something similar.
You could also keep clicking and find a different equation. Or you could go back to using Annette's.
Oh, and the equation itself is a "second order ordinary differential equation" or "second order ODE" or "second order linear ODE" or even (if you want to get really snooty and specific) a "second order linear homogeneous ODE." Which, as ODEs go, is actually fairly simple and straighforward.
Paul
