Explore x^y=y^x Function: Graphs, MatLab & Oddities

  • MATLAB
  • Thread starter cronxeh
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In summary, the conversation is about a function that is being discussed and different pictures are being shown to illustrate it. The first picture is a graph of x^y=y^x, the second one was achieved in MatLab 6.5, and the third one is a plot of x^y=-y^x. There is some confusion about the third plot due to the region it is being plotted in.
  • #1
cronxeh
Gold Member
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I'd like to resurrect the discussion of this interesting function.

Here are a few captivating pictures:

First is a graph of x^y=y^x :
http://www.imag.us/x/cronx/untitledxy.JPG [Broken]


Second one was achieved in MatLab 6.5:
http://www.imag.us/x/cronx/xyplot2.JPG [Broken]
EDU>> ezplot('x^y-y^x',[-150,-148])
I rotated the picture 90 degrees

Now this one seemed a bit odd to me.. any thoughts?


Edit:

Ok I'm freaking out here.. is my MatLab out of whack??
Plot of x^y=-y^x :
http://www.imag.us/x/cronx/wtfplot.JPG [Broken]
 
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  • #2
Maple 10.02 gives funny stuff too:

https://my.ryerson.ca/bbcswebdav/users/m4yip/gt4/xy.gif [Broken]

Here's the code I used:

Code:
restart:
with(plots):
a := implicitplot((x^y=y^x), x=-200..200, y=-200..200);
display({a});
 
Last edited by a moderator:
  • #3
Can I get a confirmation of this plot? I don't have that many applications that can do multivar plots
 
  • #4
I would say that your problem is almost entirely due to the fact that you're trying to plot in a region where x^y and y^x are defined almost nowhere.
 

1. What is the x^y=y^x function?

The x^y=y^x function is a mathematical equation that compares the values of two exponents, x and y. It is also known as the power function or the exponential function.

2. How do I graph the x^y=y^x function?

To graph the x^y=y^x function, you can use a graphing calculator or a computer program like MatLab. Plot the values of x and y on a Cartesian plane, with x as the horizontal axis and y as the vertical axis. The points where the two curves intersect are the solutions to the equation.

3. What are some oddities of the x^y=y^x function?

One oddity of the x^y=y^x function is that it has infinitely many solutions. This is because for any given value of x, there are multiple values of y that satisfy the equation. Another oddity is that the function is symmetric about the line y=x, meaning that if you switch the values of x and y, the equation will still hold true.

4. How can I use MatLab to explore the x^y=y^x function?

In MatLab, you can use the "ezplot" function to graph the x^y=y^x function. You can also use the "solve" function to find the solutions to the equation for a given range of x values. Additionally, you can use MatLab to plot the derivatives and integrals of the x^y=y^x function.

5. What real-life applications does the x^y=y^x function have?

The x^y=y^x function has applications in finance, physics, and biology. In finance, it can be used to model compound interest. In physics, it can be used to describe exponential growth or decay. In biology, it can be used to model population growth or the spread of diseases. It is also used in computer graphics to create various visual effects.

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