# Differential Equation Applications, **URL:** \ **Category:** In My Humble Opinion\ **Created:** [November 1, 2005, 11:57pm UTC](https://boards.straightdope.com/t/differential-equation-applications/328997 "2005-11-01T23:57:57Z")\ **Posts on this page:** 4\ **Page:** 1
**Author:** ![Aquafina](https://avatars.discourse-cdn.com/v4/letter/a/50afbb/32.png) [@Aquafina](https://boards.straightdope.com/u/Aquafina)\ **Post date:** [November 1, 2005, 11:57pm UTC](https://boards.straightdope.com/t/differential-equation-applications/328997/1 "2005-11-01T23:57:57Z")
Can anyone suggest me a topic for differential equation application in real life. I need a topic for my D.E’s project. It would be a bonus if it involves a system of two first order linear equations. Everything that are more complex is great, assuming that they are applicable for undergrad. Thanks ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [November 2, 2005, 12:06am UTC](https://boards.straightdope.com/t/differential-equation-applications/328997/2 "2005-11-02T00:06:37Z")
How about linear differential equations used to model [arms races](http://shakti.trincoll.edu/~pbrown/armsrace.html)? ---
**Author:** ![SlowMindThinking](https://avatars.discourse-cdn.com/v4/letter/s/dc4da7/32.png) [@SlowMindThinking](https://boards.straightdope.com/u/SlowMindThinking)\ **Post date:** [November 2, 2005, 1:42am UTC](https://boards.straightdope.com/t/differential-equation-applications/328997/3 "2005-11-02T01:42:05Z")
Well, Newton’s Laws of Motion or second order, but they seem to have wide applicability. For undergraduate work, why not look at satellite motion/control. ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [November 2, 2005, 2:19am UTC](https://boards.straightdope.com/t/differential-equation-applications/328997/4 "2005-11-02T02:19:21Z")
It shouldn’t be hard to find - differential equations are used in any situation where the _rate of change_ of a system depends on the _current state_ of the system. Which is pretty much how the whole universe works. Rate of change of temperature of an object (i.e. heat loss/gain rate) depends on the object’s temperature. Rate of change of position (i.e. velocity) depends on the object’s position (e.g. how close it is to another object). Rate of change of population depends on what the population is. Whether (and how fast) stock prices change depends on what the stock price is right now. Etc, etc…