Question

Solve the following differential equation:

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

• A. ${\tan }^{-1}y=x+\frac{x^3}{3}+C$
• B. ${\tan }^{-1}y=\frac{x^2}{2}+x+C$
• C. ${\sec }^{-1}y=x+C$
• D. None of these

Answer 1

The correct option is A ${\tan }^{-1}y=x+\frac{x^3}{3}+C$

The given differential eqaution :

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

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

Integrating both sides,

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

${\tan }^{-1}y=x+\frac{x^3}{3}+C$