Question

If $\frac{dy}{dx}=\frac{xy+y}{xy+x}$, then the solution of the differential equation is?

Answer 1

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

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

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

$\Rightarrow y+lny=x+lnx+C$