# System of ODE for functions with different origins

• FrankST
In summary, the conversation discusses a system of coupled ODE with a shift in the origins for Y1 and Y2. The speaker is seeking advice on how to solve this system, and mentions using the eigenvalue method. The solution proposed is to solve without the shift and then translate at the end.
FrankST
Hi,

I have a system of coupled ODE like:

a1 * Y1" + a2 * Y2" + b1 * Y1 + b2 * Y2 = 0
a2 * Y1" + a3 * Y2" + b2 * Y1 + b3 * Y2 = 0

I know for example by eigenvalue method I can solve it, but here is the issue: Y1 = f1 (x - a) and Y2 = f2 ( x - b). In the other word there is a shift between the coordinates that Y1 and Y2 are evaluated in. Now, I am wondering if you have any idea how I can solve this system of ODE.

Thanks a lot,

If the problem is the shift in the origins, first solve with the origins unshifted and at the end make a translation.

## 1. What is a system of ODE for functions with different origins?

A system of ODE (ordinary differential equations) for functions with different origins is a set of equations that describe the relationship between multiple functions that have different starting points or origins. These equations are used to model dynamic systems and predict their behavior over time.

## 2. How does a system of ODE for functions with different origins differ from a regular system of ODE?

The main difference is that in a regular system of ODE, all the functions share the same starting point or origin. In a system of ODE for functions with different origins, each function has its own unique starting point, which adds complexity to the equations and requires additional techniques to solve.

## 3. What are some common applications of systems of ODE for functions with different origins?

These types of systems are commonly used in physics, engineering, and economics to model and analyze various dynamic systems. They can be applied to study the behavior of populations, chemical reactions, and electrical circuits, among other things.

## 4. How are systems of ODE for functions with different origins solved?

There are various methods for solving these types of systems, including numerical techniques such as Euler's method and Runge-Kutta methods, as well as analytical methods such as Laplace transforms and separation of variables. The specific method used depends on the complexity of the system and the desired level of accuracy.

## 5. What are some challenges associated with working with systems of ODE for functions with different origins?

One of the main challenges is finding an appropriate mathematical model to accurately represent the system being studied. This requires a deep understanding of both the system and the underlying mathematical principles. Additionally, solving these systems can be computationally intensive and may require advanced numerical techniques.

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