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Q.

The solution of $(x^{2} - y^{2} x^{2}) (dy / dx) + (y^{2} + x^{2} y^{2}) = 0$ is

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a

$x - \frac{1}{x} + y - \frac{1}{y} = c$

b

$x + \frac{1}{x} - y - \frac{1}{y} + c = 0$

c

$x + \frac{1}{x} + y + \frac{1}{y} + c = 0$

d

$x - \frac{1}{x} - y - \frac{1}{y} = c$

answer is D.

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Detailed Solution

$(x^{2} - y^{2} x^{2}) \frac{dy}{dx} + (y^{2} + x^{2} y^{2}) = 0$

$(\frac{1 - y^{2}}{y^{2}}) dy + (\frac{1 + x^{2}}{x^{2}}) dx = 0$

Integrating $x - \frac{1}{x} - y - \frac{1}{y} = c$

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