Question

Solve the following differential equation:

$dy=(1+x+y+xy)dx$

Answer 1

Consider the given differential equation

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

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

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

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

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

${\log }_c|1+y|=x+\frac{x^2}{2}+C$