If(x^2+y^2)^2=xy, find dy dx . - Vidyadip

Question

$\text{If}(\text{x}^2+\text{y}^2)^2=\text{xy, find}\ \frac{\text{dy}}{\text{dx}}.$

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Answer

$(\text{x}^2+\text{y}^2)^2=\text{xy}$
$2(\text{x}^2+\text{y}^2)\Big[2\text{x}+2\text{y}\frac{\text{dy}}{\text{dx}}\Big]=\text{x}\frac{\text{dy}}{\text{dx}}+\text{y}$
$4\text{x}(\text{x}^2+\text{y}^2)+4\text{y}(\text{x}^2+\text{y}^2)\frac{\text{dy}}{\text{dx}}=\text{x}\frac{\text{dy}}{\text{dx}}+\text{y}$
$4\text{x}(\text{x}^2+\text{y}^2)-\text{y}=\frac{\text{dy}}{\text{dx}}\big[\text{x}-4\text{y}(\text{x}^2+\text{y}^2)\big]$
$\frac{\text{dy}}{\text{dx}}=\frac{4\text{x}(\text{x}^2+\text{y}^2)-\text{y}}{\text{x}-4\text{y}(\text{x}^2+\text{y}^2)}$

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