Fun with DEs

[-N-]

Solve the following, anyone?
<pre>
[1 0 1] [e^t ]
X' = [0 0 2] X + [0 ]
[0 0 1] [e^-t]
</pre>
X and X' are vectors, obviously. I got
<pre>
[t] [1] [0]
e^t(c1 [2] + c2 [0]) + c3 [1]
[1] [0] [0]
</pre>
for the undriven case, which I'm fairly certain of, and
<pre>
[te^t(1+K3) + e^t(K1) + .25e^-t]
[2e^t(K3) + e^-t + (K2 - 2K3) ]
[e^t(K3) - .5e^-t ]
</pre>
for the driven case.

Take your best shot; I guess I'm just looking to make sure I'm right.

[Ism]

Is this supposed to make sense? And how old r u?

[Mercen-X]

Do your OWN DMN homework, lazy@ss! lol . . . the answer is 5

[Devourment]

Solve the following, anyone?
<pre>
[1 0 1] [e^t ]
X' = [0 0 1] X + [0 ]
[0 0 2] [e^-t]
</pre>
X and X' are vectors, obviously. I got
<pre>
[t] [1] [0]
e^t(c1 [2] + c2 [0]) + c3 [1]
[1] [0] [0]
</pre>
for the undriven case, which I'm fairly certain of, and
<pre>
[te^t(1+K3) + e^t(K1) + .25e^-t]
[2e^t(K3) + e^-t + (K2 - 2K3) ]
[e^t(K3) - .5e^-t ]
</pre>
for the driven case.

Take your best shot; I guess I'm just looking to make sure I'm right.Is this work you want other people to do for you?

[Ism]

If you explain the theory and what the :skull::skull::skull::skull: it is then I would gladly do it for you.

[Meat Puppet]

I read this thread, and my heart exploded. (I blame fast food)

[Psychotic]

Oh alright, I'll say it so that no-one else has to: 42.

Now let's get on with life!

[Resha]

MATHS IS BAD. WHATEVER THAT WAS IS BAD. I THINK IT'S EITHER MATHS OR PHYSICS! :weep:

[Caspian]

That's vector analysis, and the only person here who might have a snowball's chance in hell of helping you with it is Dingo Jellybean.

Stop inflicting college-level math concepts on these 13-18 year old forumers, it's pointless.

[Samuraid]

I took differential equations 2 years ago...and I don't remember how to do that. :(

[Caspian]

I took differential equations 2 years ago...and I don't remember how to do that. :(

Because that's not a differential equation?

=P

[Rainecloud]

The thread title is misleading. This isn't fun. :(

[Skogs]

Um... solve for what?

[theundeadhero]

You lured me in with fun, then befuddled me :(


2.9999~ = 3 ;)

[Samuraid]

I took differential equations 2 years ago...and I don't remember how to do that. :(

Because that's not a differential equation?

=P

Actually, it is in a way. Notice the X and X'. The equation expresses a relationship between X and it's derivative, thus it is a differential equation.

[rubah]

Ha. we have enough trouble doing vectors that just deal with *two* coordinates.

that mess is big and scary.

[escobert]

4

Give me a cookie :D

[Apollo]

So...many...numbers! :Oo: *explodes*

[Shlup]

What math is that from? BJ likes math.

[-N-]

Systems of linear differential equations with driving terms. I've kinda given up on people here trying to figure it out anyways, and I checked partially with MATLAB and Maple and ODE Architect, so whatever.

[Yamaneko]

I'm going to start discussing <u>The Great Gatsby</u> if you guys don't knock off the math threads.

[Leeza]

Please do, Yams. I need to know what happens in Chapter 2. :)

[-N-]

We can start a new thread for discussion on topics that are not about solving linear systems of ODEs with driving terms, thanks. :D < / modwhore >
Is no one else going to try this? :(

[theundeadhero]

I often wonder how this applies to the real world, or if it's just because a bunch of old men with funny mustaches thought it would be funny.

[-N-]

Systems of DEs have a lot of applications in engineering systems and control theory. Often, when designing a system, be it anything from an actuator that controls spoiler movement in aircraft to microsurgery robots (nanomachines and molecular engineering are seriously ALL controls), it is wise to start with an ideal mathematical model that you want to fulfill with physical elements.

A lot of computer basics rest on DEs as well, and approximating them with finite state machines. While the above problem concerns continuous states (such as x' and x), FSMs discretize the process, and essentially act as a registry for values that are passing through a processor.

Another application I know of that I'm not involved in is species survival and ecological modeling. I had to do a little bit of it, but I don't know the details of how it works as well as other things.

[Samuraid]

Differential Equations are integral (full pun intended) to many technical fields. (I'm in Computer Engineering and we sometimes use first and second order DEs to describe some electrical circuits.)

However, I'm sure that most people here on the forums either don't use DEs regularly at all or don't really care about them. (or both :p)