Question

Solution of the equation $(1+x^2)dy=(1+y^2)dx$ is-

• A. y - x = c(1 + xy)
• B. y- x = c(1 - xy)
• C.
• D.

Answer 1

Answer: (A), (C), (D)

The correct options are
A

y - x = c(1 + xy)

C

D

$\int \frac{dx}{1+y^2}=\int \frac{dy}{1+x^2}$

${\tan }^{-1}y={\tan }^{-1}x+c$

or $\frac{\pi }{2}-co{t}^{-1}y={\tan }^{-1}x+c$

or ${\tan }^{-1}x+co{t}^{-1}y=\frac{\pi }{2}-c$

${\tan }^{-1}y-{\tan }^{-1}x=c$

$\Rightarrow {\tan }^{-1}\left(\frac{y-x}{1+xy}\right)=c\Rightarrow \frac{y-x}{1+xy}=tanc=k$