Find the general solution of the differential equations `(dy)/(dx)=(1+x^2)(1+y^2)`

Explanation

Given

`frac{d y}{d x}=(1+x^{2})\left(1+y^{2})`

By rearranging the terms

`frac{d y}{1+y^{2}}=(1+x^{2}) d x`

Now by integrating both sides w.r.t `x`

`int \frac{d y}{1+y^{2}}=\int(1+\{x}^{2}\) d x+c`

We get

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