If y = x +1 x , show that 2x dy dx +y=2 x . - Vidyadip

Question

$\text{If y = }\sqrt{\text{x}}+\frac{1}{\sqrt{\text{x}}},\text{ show that }\text{2x}\frac{\text{dy}}{\text{dx}}+\text{y}=2\sqrt{\text{x}}.$

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Answer

Getting $\frac{\text{dy}}{\text{dx}}=\frac{1}{2\sqrt{\text{x}}}-\frac{1}{\text{2x}\sqrt{\text{x}}}$
$\therefore\text{ 2x}\frac{\text{dy}}{\text{dx}}=\sqrt{\text{x}}-\frac{1}{\sqrt{\text{x}}}$
$\text{ 2x}\frac{\text{dy}}{\text{dx}}+\text{y}=\Bigg(\sqrt{\text{x}}-\frac{1}{\sqrt{\text{x}}}\Bigg)+\Bigg(\sqrt{\text{x}}+\frac{1}{\sqrt{\text{x}}}\Bigg)=2\sqrt{\text{x}}.$

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