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Question

The solution of the differential equation $x d y minus y d x equals left parenthesis square root of x to the power of 2 end exponent plus y to the power of 2 end exponent right parenthesis end root d x$ is

$y - \sqrt{x^{2} + y^{2}} = c x^{2}$
$y + \sqrt{x^{2} + y^{2}} = c x^{2}$
$y + \sqrt{x^{2} + y^{2}} + c x^{2} = 0$
None of these

The correct answer is: $y plus square root of x to the power of 2 end exponent plus y to the power of 2 end exponent end root equals c x to the power of 2 end exponent$

It is a homogenous equation, solve it by putting $y equals v x$ and $fraction numerator d y over denominator d x end fraction equals v plus x fraction numerator d v over denominator d x end fraction$ .

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