Is this differential system of equations *coupled*?

In summary, a coupled system of equations is one in which the equations are dependent on each other and cannot be solved separately. This means that the solution of one equation will affect the solution of the other equation. To determine if a system of equations is coupled, check if there are at least two equations that share one or more variables. The advantages of a coupled system of equations include the ability to model and analyze complex systems and consider the relationships between variables. However, a coupled system of equations requires a different approach for solving compared to a non-coupled system, as the equations must be solved simultaneously. Real-life examples of coupled systems of equations include the predator-prey model, the Lotka-Volterra equations, and the SIR model
  • #1
asgard
1
0
I am struggling with whether or not to define the following system as coupled:
Using LaTeX (reload if it doesn't display properly)

[itex]\ddot{x}+A*x=0[/itex]

[itex]\ddot{y}+A*y=0[/itex]

[itex]\ddot{z}+A*z=0[/itex]​

where A is a known constant equal to [itex]A=\sqrt{x^2+y^2+z^2}[/itex]

So, what do you think?
 
Last edited:
Physics news on Phys.org
  • #2
Yes, it is a coupled system. Even if A is constant so the solution is apparently restricted to a sphere, still the value of x depends on y and z. I don't 100% guarantee this answer though.
 
  • #3
Yes, these equations are coupled.
 

FAQ: Is this differential system of equations *coupled*?

What does it mean for a system of equations to be "coupled"?

When a system of equations is "coupled", it means that the equations are dependent on each other and cannot be solved separately. This means that the solution of one equation will affect the solution of the other equation.

How can I determine if a system of equations is coupled?

A system of equations is considered coupled if there are at least two equations that share one or more variables. This means that the variables in these equations are not independent and cannot be solved separately.

What are the advantages of having a coupled system of equations?

A coupled system of equations allows us to model and analyze more complex and interconnected systems. It also allows us to consider the relationships between different variables and how they affect each other.

Can a coupled system of equations be solved using the same methods as a non-coupled system?

No, a coupled system of equations requires a different approach for solving compared to a non-coupled system. The equations must be solved simultaneously, taking into account the dependencies between variables.

Are there any real-life examples of coupled systems of equations?

Yes, there are many real-life examples of coupled systems of equations. Some examples include the predator-prey model in ecology, the Lotka-Volterra equations in population dynamics, and the SIR model in epidemiology. These systems involve multiple variables that are interdependent and cannot be solved separately.

Similar threads

I A common 2nd order ODE from dynamics but....
Replies
8
Views
2K
I When is an ODE (numerically) reversible in time?
Replies
4
Views
421
I Can I Differentiate Both Sides to Solve y in y^2=ln(1-y^2)?
Replies
2
Views
2K
I Finding Max and Min Extremes of a Function with Second Derivatives Equal to Zero
Replies
1
Views
2K
I Runge-Kutta 4 w/ some sugar on the top: How to do error approximation?
2
Replies
65
Views
4K
I Fundamental matrix of a second order 2x2 system of ODEs
Replies
2
Views
2K
I On sub and super solutions: Teschl and others
Replies
5
Views
1K
How should I find the equilibrium points and the general equation?
Replies
3
Views
603
I Find Practical Resonance Frequencies in Linear Differential Equations
Replies
1
Views
2K
I Helmholtz Equation in Cartesian Coordinates
Replies
11
Views
2K

Hot Threads

Recent Insights

Back
Top