The solution of the differential equation \(\displaystyle\frac{dy}{dx}= (1 + x^2)(1 + y^2)\) is (Here C is an arbitrary constant)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\tan^{-1}y-x-\displaystyle\frac{x^3}{3}=C\)
The variables are separable. Dividing by \(1 + y^2\):
\( \displaystyle \frac{dy}{1 + y^2} = (1 + x^2)\,dx \)
Integrating both sides:
\( \displaystyle \int\frac{dy}{1 + y^2} = \int(1 + x^2)\,dx \)
\( \displaystyle \tan^{-1}y = x + \frac{x^3}{3} + C \)
\( \displaystyle \tan^{-1}y - x - \frac{x^3}{3} = C \)
NCERT (2026-27 edition):
Differential Equations with Variables Separable
