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Category: Differential Equation

Find-dy-dx-x-y-y-x-

Question Number 26983 by chernoaguero@gmail.com last updated on 31/Dec/17 $$\mathrm{Find}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\:\:\: \\ $$$$\:\:\:\:\mathrm{x}^{\mathrm{y}} =\mathrm{y}^{\mathrm{x}} \\ $$ Answered by mrW1 last updated on 31/Dec/17 $${y}\:\mathrm{ln}\:{x}={x}\:\mathrm{ln}\:{y} \\ $$$${y}'\:\mathrm{ln}\:{x}+\frac{{y}}{{x}}=\mathrm{ln}\:{y}+\frac{{x}}{{y}}\:{y}'…