Question

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

Answer 1

Finding General solution
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
We get,

$\int \frac{dy}{1+y^2}$

$=\int (1+x^2)dx$

(Since,

$\int \frac{dy}{1+y^2}={\tan }^{-1}y+C)$

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

Final Answer:
Hence, the required general solution is

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