What Physical Models could these ODES represent?

[pat666]

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.

 

[Mark44]

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).

 

[pat666]

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

 

[epenguin]

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.