What Physical Models could these ODES represent?

Click For Summary

Homework Help Overview

The discussion revolves around a set of ordinary differential equations (ODEs) presented in a second-year engineering mathematics context. Participants are exploring potential real-world applications or physical models that these equations might represent, referencing concepts such as RLC circuits, springs, and beam deflections.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants are questioning the applicability of the given ODEs to real-world phenomena, with some expressing skepticism about their relevance to traditional physical models like RLC circuits or spring systems. Others are considering broader contexts, such as chemical or biological systems, where these equations might apply.

Discussion Status

The discussion is ongoing, with participants sharing their thoughts on the types of models that could be represented by the equations. Some have noted the challenge of aligning the equations with known physical systems, while others are exploring creative interpretations of the equations' forms.

Contextual Notes

Participants are under the constraint of an assignment that requires both analytical and computational solutions to the ODEs, along with a relevant physical model for bonus marks. There is an emphasis on not seeking direct solutions to the equations themselves.

pat666
Messages
703
Reaction score
0

Homework Statement



(2xy-5)dx+(x^2+y^2)dy=0, y(3)=1

(2x+y^2)dx+4xy dy=0, y(1)=1

x^3y'+xy=x, y(1)=2

y'(t)=-4y+6y^3

We're doing these in 2nd yr engineering Math and I have heard the Lecturer say they are useful across all disciplines. I've heard him suggest RLC circuits, springs with driving forces and something about beam deflections.

My question is what type of things could these 4 ode's be used to model in the real world?

P.S. I don't want help solving them, already got that and solved them all.
 
Physics news on Phys.org
pat666 said:

Homework Statement



(2xy-5)dx+(x^2+y^2)dy=0, y(3)=1

(2x+y^2)dx+4xy dy=0, y(1)=1

x^3y'+xy=x, y(1)=2

y'(t)=-4y+6y^3

We're doing these in 2nd yr engineering Math and I have heard the Lecturer say they are useful across all disciplines. I've heard him suggest RLC circuits, springs with driving forces and something about beam deflections.

My question is what type of things could these 4 ode's be used to model in the real world?

P.S. I don't want help solving them, already got that and solved them all.
I could be wrong, but I don't think that any of these model any physical phenomena, and certainly not RLC circuits or springs. The differential equations for RLC circuits and spring/mass/damper systems tend to be 2nd order, linear, and either homogeneous (no forcing function) or nonhomogeneous (forced).
 
That's interesting, we have an assignment which is solve these analytically and with mathematica. But there's bonus marks for finding a " relevant model of a physical system or application". I've been having trouble matching theses up...

Thanks
 
I have not thought any example through, but you can get square terms or simple product (xy) when something depends on the frequency of things meeting, so you could maybe invent a chemical, biological or social/economic science scenario. You can also get these products and many others out of chemical and biological equilibria established on a more rapid time-scale than that of your d.e. And you can get (constant minus something) when you eliminate a variable by a conservation law.
 
Last edited:

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
3
Views
2K
  • · Replies 25 ·
Replies
25
Views
2K
Replies
4
Views
3K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 24 ·
Replies
24
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
Replies
11
Views
2K