find solution of dy/dx=x(1+y) using separation of variables

 Find solution of $\frac{dy}{dx}=x(1+y)$ using separation of variables

Solution:

We have given that

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

Now, we have

$\frac{dy}{(1+y)}=xdx$

Now, integrating both sides

                                                               $\int{\frac{dy}{(1+y)}}=\int{xdx}+c$

                                                               ${ln(1+y)}=\frac{x^2}{2}+c$

Where $c$ is integration constant.

Answer.