Looking for a function in system of DE

In summary, a function in a system of differential equations (DE) is a mathematical relationship that describes the behavior of the system over time. To find a function in a system of DE, one must solve the equations simultaneously using methods such as separation of variables, substitution, or integrating factor. Finding a function in a system of DE is important for understanding and predicting the system's behavior, and real-world systems often have multiple functions interconnected and influencing each other. There are various tools and software, such as WolframAlpha, MATLAB, and Maple, that can assist in finding a function in a system of DE by using numerical and analytical methods.
  • #1
sludger13
83
0
I'm looking for prescription of function [itex]f[/itex] with behavior:
attachment.php?attachmentid=70294&stc=1&d=1401779566.png


putted in this system of DE solving some simple functions [itex]r_{1}(x)[/itex] and [itex]r_{2}(x)[/itex]:
[itex]\frac{d^{2}r_{2}(x)}{dx^{2}}=\frac{f(r_{2}(x)-r_{1}(x))}{C}[/itex]
[itex]\frac{d^{2}r_{1}(x)}{dx^{2}}=-\frac{f(r_{2}(x)-r_{1}(x))}{K}[/itex]

[itex]r_{2}(x)-r_{1}(x)>0;f(r_{2}(x)-r_{1}(x))>0;C,K>0[/itex]
 

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  • #2
Why not a straight line?
 
  • #3
3.31143 - 1.37286 x + 0.135714 x^2

fits more or less the lower curve
 

FAQ: Looking for a function in system of DE

1. What is a function in a system of DE?

A function in a system of differential equations (DE) is a mathematical relationship that describes the behavior of the system over time. It is typically expressed as an equation involving the variables and their derivatives.

2. How do you find a function in a system of DE?

To find a function in a system of DE, you need to solve the equations simultaneously. This can be done by using various methods such as separation of variables, substitution, or using an integrating factor. The specific method will depend on the type of DE and its complexity.

3. What is the importance of finding a function in a system of DE?

Finding a function in a system of DE is important because it allows us to understand and predict the behavior of the system over time. This is crucial in many scientific fields, such as physics, engineering, and biology, where systems are often described by DE.

4. Can a system of DE have multiple functions?

Yes, a system of DE can have multiple functions. In fact, most real-world systems are described by multiple equations that are interconnected and influence each other. This results in a system of DE with multiple functions that describe the behavior of the system.

5. Are there any tools or software that can help in finding a function in a system of DE?

Yes, there are various tools and software that can assist in finding a function in a system of DE. Some examples include WolframAlpha, MATLAB, and Maple. These tools use numerical and analytical methods to solve DE and find the corresponding functions.

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