The solution of the differential equation $\frac{dy}{dx}= (1 + x^2)(1 + y^2)$ is (Here C is an arbitrary constant)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\tan^{-1}y-x-\frac{x^3}{3}+=C$
$\frac{dy}{dx}=(1+x^{2})(1+y^{2})$
$\Rightarrow \frac{dy}{1+y^{2}}=(1+x^{2})\,dx$
$\Rightarrow \tan^{-1}y= x+\frac{x^{3}}{3}+C$
$\displaystyle y=\tan\!\left(x+\frac{x^{3}}{3}+C\right)$