# Differential Equations Paper

Hi all,

As part of my differential equations class, I must choose a real-world event that can be modeled through a system of ordinary linear differential equations and write a five page paper on it. My professor was vague on the requirements but basically wants us to solve the equations, plot them on mathematica, and analyze the results.

A couple examples of the expected difficulty level of the ODE model are (1) describing the quantitative relationship among lion, zebra, and hyena populations in the African Savannah (the zebra population at a given time depends upon the population of lions and hyenas) and (2) describing the quantitative relationship amoung three interconnected tanks with various concentrations of a particular solute (ex. all three tanks are being filled by an exterior hose with a unique concentration of solution at a unique rate. If all three tanks are connected together by pipes with the solution flowing among tanks as well as entering through the three hoses and exiting the entire tank systems through a hole in each tank, at what rate do the concentrations of each tank change?)

Anyway, I was wondering if anyone had any good ideas for an event to model. My major is electrical engineering, and I am sure there are numerous instances of differential equations in this field. However, I have not began any engineering classes yet so their applicability to that subject is unknown to me at this point. So if someone has any interesting and suitable ideas (preferably involving EE), I would love to hear them.

Thanks

If you are an EE major you could harmonic oscillators, which occur in LRC circuits and are pretty easy to cover.

ranger
Gold Member
I had to do a similar project. I chose to model simple harmonic motion of a spring:
my'' + cy' + ky = f(t)
m = mass on spring
c = damping
k = spring constant
f(t) = external force.
y'', y', and y have there usual meanings.

Takes little time to implement and its a good example of an ODE application.