Q. The general solution of the differential equation $\left( 1 + y^{2} \right)dx + \left( 1 + x^{2} \right)dy = 0$ is
A) $x - y = c(1 - xy)$
B) $x - y = c(1 + xy)$
C) $x + y = c(1 - xy)$
D) $x + y = c(1 + xy)$
Explanation
(c)
Given, $\frac{dx}{1 + x^{2}} + \frac{dy}{1 + y^{2}} = 0$
$\Rightarrow$ $\tan^{- 1}x + \tan^{- 1}y = \tan^{- 1}c$ [integrating]
$\Rightarrow$ $\frac{x + y}{1 - xy} = c$
$\Rightarrow$ $x + y = c(1 - xy)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.