What Physical Models could these ODES represent?

In summary, the four given differential equations can be used to model various physical systems and applications, such as chemical and biological equilibria, social and economic scenarios, and systems with conservation laws. They may also have relevance in RLC circuits and springs with driving forces, but these may not be direct applications.
  • #1
pat666
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Homework Statement



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

[tex] (2x+y^2)dx+4xy dy=0, y(1)=1[/tex]

[tex] x^3y'+xy=x, y(1)=2 [/tex]

[tex] y'(t)=-4y+6y^3 [/tex]

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.
 
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  • #2
pat666 said:

Homework Statement



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

[tex] (2x+y^2)dx+4xy dy=0, y(1)=1[/tex]

[tex] x^3y'+xy=x, y(1)=2 [/tex]

[tex] y'(t)=-4y+6y^3 [/tex]

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).
 
  • #3
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
 
  • #4
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:

Related to What Physical Models could these ODES represent?

What Physical Models could these ODES represent?

1. What are ODES and how are they used in physical modeling?

ODES, or Ordinary Differential Equations, are mathematical equations used to model physical systems by describing the relationship between a system's variables and their rates of change over time. They are widely used in physics, engineering, and other scientific fields to study and predict the behavior of various physical phenomena.

2. Can ODES be used to model any system or are they limited to certain types of phenomena?

ODES can be used to model a wide range of physical systems, including mechanical, electrical, biological, and chemical systems. However, their applicability may be limited in cases where the system is highly complex or involves non-linear relationships between variables.

3. How accurate are physical models based on ODES?

The accuracy of a physical model based on ODES depends on the accuracy of the equations used and the assumptions made about the system. In some cases, simplifications or approximations may need to be made in order to create a solvable ODE, which can affect the accuracy of the model. Additionally, the accuracy of the model may also depend on the quality and quantity of data used to calibrate and validate the model.

4. Are there any limitations to using ODES in physical modeling?

One limitation of using ODES in physical modeling is that they may not be able to capture all aspects of a complex system. For example, ODES may not be able to account for external factors or random variations that can affect the behavior of a system. Additionally, the assumptions made in creating the ODE may not always accurately reflect the real-world system, leading to inaccurate predictions.

5. How do scientists determine the appropriate ODES to use for a given physical model?

Choosing the appropriate ODES for a physical model involves a combination of theoretical understanding, experimental data, and trial and error. Scientists may also use knowledge from other fields, such as physics or mathematics, to inform their choice of ODES. Additionally, the ODES may need to be modified or refined as the model is tested and validated against real-world data.

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