Q78 / 120 · VITEEE 2012 · Mathematics

The general solution of the differential equation $\left(1+y^{2}\right) d x+\left(1+x^{2}\right) d y=0$ is

  • A
    $x-y=C(1-x y)$
  • B
    $x-y=C(1+x y)$
  • Correct answer
    C
    $x+y=C(1-x y)$
  • D
    $x+y=C(1+x y)$

Solution

$\left(1+y^{2}\right) d x+\left(1+x^{2}\right) d y=0$ $\Rightarrow \frac{d x}{1+x^{2}}+\frac{d y}{1+y^{2}}=0$ On integrating, we get $$ \begin{array}{l} \tan ^{-1} x+\tan ^{-1} y=\tan ^{-1} C \\ \Rightarrow \frac{x+y}{1-x y}=C \\ \Rightarrow x+y=C(1-x y) \end{array} $$

Hence, the correct answer is option: 'C'.

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