Question

For the differential equations, find the general solution:$\frac {dy}{dx} =(1+x^2)(1+y^2)$

Answer 1

The given differential equation is:

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

$⇒\frac {dy}{1+y^2}=(1+x^2)dx$

Integrating both sides of this equation, we get:

$∫\frac {dy}{1+y^2}=∫(1+x^2)dx$

$⇒tan^{-1}y=∫dx+∫x^2dx$

$⇒tan^{-1}y=x+\frac {x^3}{3}+C$

This is the required general solution of the given differential equation.