Question

The solution of the differential equation $(1 + x^{2})\frac{dy}{dx} = x(1 + y^{2})$ is

• A. $2\tan^{- 1}y = \log(1 + x^{2}) + c$
• B. $\tan^{- 1}y = \log(1 + x^{2}) + c$
• C. $2\tan^{- 1}y + \log(1 + x^{2}) + c = 0$
• D. None of these

Answer 1

Answer: (A)

$2\tan^{- 1}y = \log(1 + x^{2}) + c$

Answer 2

Separating the variables, we can re-write the given differential equation as

$\frac{xdx}{1 + x^{2}} = \frac{dy}{1 + y^{2}}$ ⇒ $\int_{}^{}{\frac{2xdx}{1 + x^{2}} = 2\int_{}^{}\frac{dy}{1 + y^{2}}}$

⇒ $2\tan^{- 1}y = \log_{e}(1 + x^{2}) + c$