Parametric solution to: x^y = y^x
Calculus
Level
3
Consider the solution set of this equation in Quadrant I. This set includes the line y=x, and another differentiable curve. Find a parametric representation of this curve. Write this parametrization in the form (f(t), g(t)).
(t^(1/(t-1)),t^(t/(t-1))
((t/(t-1))^t,(1/(t-1))^t)
(t^(t/(1-t)),t^(1/(1-t))
(t^(e/(t-e)),t^(t/(t-e))
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1 solution
I don't have time to write out my solution here, but here's a link to a plot of the actual parametrization: https://www.desmos.com/calculator/zyjku89imw