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Maths-

General

Easy

Question

The solution of $x squared fraction numerator d y over denominator d x end fraction minus x y equals 1 plus cos space y over x$ is

$\tan \frac{y}{2 x} = c - \frac{1}{2 x^{2}}$
$\tan \frac{y}{x} = c + \frac{1}{x}$
$\cos (\frac{y}{x}) = 1 + \frac{c}{x}$
$x^{2} = (c + x^{2}) \tan \frac{y}{x}$

hint Hint:

In the question we have to integrate the given function.

The correct answer is: $tan space fraction numerator y over denominator 2 x end fraction equals c minus fraction numerator 1 over denominator 2 x squared end fraction$

$x squared fraction numerator d y over denominator d x end fraction minus x y equals 1 plus cos space y over x rightwards double arrow x squared fraction numerator d y over denominator d x end fraction minus x y equals 2 cos squared fraction numerator y over denominator 2 x end fraction rightwards double arrow fraction numerator 1 over denominator cos squared begin display style fraction numerator y over denominator 2 x end fraction end style end fraction open square brackets x squared. fraction numerator d y over denominator d x end fraction minus x y close square brackets equals 2 rightwards double arrow 1 half s e c squared fraction numerator y over denominator 2 x end fraction open square brackets fraction numerator x. begin display style fraction numerator d y over denominator d x end fraction end style minus y over denominator x squared end fraction close square brackets equals 1 over x cubed rightwards double arrow fraction numerator d over denominator d x end fraction tan fraction numerator y over denominator 2 x end fraction equals 1 over x cubed O n space i n t e g r a t i n g space w e space g e comma integral fraction numerator d over denominator d x end fraction tan fraction numerator y over denominator 2 x end fraction d x equals integral 1 over x cubed d x tan fraction numerator y over denominator 2 x end fraction equals C minus fraction numerator 1 over denominator 2 x squared end fraction$

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