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I know the basic graph and shifting the graphs. But I have a special equation. I will explain the specialty of the functions later. Okay...let me say the specialty. This function has infinitely many solutions. I would like to know the GRAPH of the function. I can't draw the graph of this function. Please use computer and show me the picture/ graph of the following functions. Once again thank you for this wonderful site and members of this site.

function is: $x^y$ - $z^2$x + $z^2$y - $y^x$ = 0

Also, I want to know that, what kind of function it is? I mean, is it elliptic curve? or something else....

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    Sir, I am using MATLAB software. Unfortunately, I am not able to draw. Please could you draw this graph...2012-03-17

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$\begin{align} &&x^y-z^2 x+z^2 y-y^x&=0 \\ &\implies&x^y-y^x-z^2(x-y)&=0 \\ &\implies&x^y-y^x&=z^2(x-y) \\ &\implies&\frac{x^y-y^x}{x-y}&=z^2 \\ &\implies&z=\pm\sqrt{\frac{x^y-y^x}{x-y}}&=\pm\frac{\sqrt{x^y-y^x}}{\sqrt{x-y}} \\ \end{align}$

Applying WolframAlpha to $z=\frac{\sqrt{x^y-y^x}}{\sqrt{x-y}}$ (just the $+$ part, not the $-$ part) shows several visualizations.