General solution of differential equation is

JEE MainMathematicsModerateDifferential equation

General solution of differential equation
$x^{2}(x + y\frac{dy}{dx}) + (x\frac{dy}{dx} - y)\sqrt{x^{2} + y^{2}} = 0$
is

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\frac{xdx + ydy}{\sqrt{x^{2} + y^{2}}} + \frac{xdy - ydy}{x^{2}} = 0

\frac{1}{2}\frac{d(x^{2} + y^{2})}{\sqrt{x^{2} + y^{2}}} + d(\frac{y}{x}) = 0

\Rightarrow \frac{1}{2}\frac{\sqrt{x^{2} + y^{2}}}{\frac{1}{2}} + \frac{y}{x} = c

Source: Grass-G / M-13 Mathematics Paper 4 Nov.docx

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