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.