Differential Equations in engineering

[gordilloedwin]

Hi there..

I'm a second semester student and I was asked by my teacher to ask some engineers and scientist about three problems in which differential equations are used, I need to solve them myself using the methods I already know. they can be simple ones because I need to deliver the project in three days.
Since i know there has to be some awesome engineers in here, I please ask you to propose three problems which i would need to use D.E. , they have to be problems i may find in analizing something like a circuit or a material.. i don't know but please keep it "simple", am just in second semester but i do know how to work on D.E. but i have never take them into real life.
The hardest problem for me would be to mathematically modelate the problem.. So there's my request.
Oh .. and if you can tell me if you think D.E. are important and if so, why you think so, your name and the class you teach.. err, and a little initial thought on how to correctly modelate your problem( the initial equiation ). i know many use them as t=0 and from there well you know .. I was not allowed to use any of the problems in Stewart/Calculus nor the Larson/Calculus books :(

I hope information was clear :P

thanks in advance
Edwin Gordillo
IPN

 

[Defennder]

Well, in order to help you, I suppose we must first know how much you currently know about DEs. Do you know how to solve 2nd order homogenous linear ODEs? Eg. y'' + 2y' + y =0.

For first order ODEs, do you know the method of solving by integrating factors, Bernoulli DEs, exact differential equations?

 

[gordilloedwin]

Ok .. here's what i know
variables-separable
homogeneous
exact
not exact- integration factor?
Lineal
Bernoulli
Ricatti

the one you showed me is solved by first writing a "like-equiation" as m^2 + 2m+1 = 0 and i can even solve the ones that have a function g(x) .. for instance y'' + 2y' + y = e^x
Im also able to solve 2nd order lineal homogeneous using power series.. please excuse my english as am not a native speaker.

anyways is pretty much what I can do , however using power series is kind of .. a more extensive process and I don't have as much time :(

Thanks!

 

[Defennder]

Well a quick suggestion for a 2nd order linear homogenous ODE would be to solve for a circuit consisting of a inductor, capacitor and resistor as well as a voltage source all connected in series.

If you want more suggestions, this link helps a lot:
http://www.sosmath.com/diffeq/diffeq.html

 

[gordilloedwin]

Wow... this is great! thanks