Question

Solve : $\frac{dy}{dx}=1+x+y+xy$

Answer 1

The given equation can be written in the form
$\frac{dy}{dx}=(1+x)+y(1+x)$
$\Rightarrow \frac{dy}{dx}=(1+x)(1+y)$
$\Rightarrow \frac{dy}{1+y}=(1+x)dx$
On integrating, we have
$\log (1+y)=x+\frac{x^2}{2}+c$, which is the required solution.