Question

Find general solution of differential equation $\frac{dy}{dx}=\frac{1+y^2}{1+x^2}$

Answer 1

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

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

Integrating, we get $\int \frac{dy}{1+y^2}=\int \frac{dx}{1+x^2}$

$\therefore ta{n}^{-1}y=ta{n}^{-1}x+c$