# Math Help - separable differential eqn

1. ## separable differential eqn

show that (xy+y)dx-(xy-x)dy=0 is a seperable differential eqn
and find a solution that satisfies the condition y(1)=2

2. Originally Posted by samdmansam
show that (xy+y)dx-(xy-x)dy=0 is a seperable differential eqn
and find a solution that satisfies the condition y(1)=2
$y (x + 1) \, dx - x (y - 1) \, dy = 0$

$\Rightarrow \frac{x+1}{x} \, dx - \frac{y-1}{y} \, dy = 0$

$\int \frac{x+1}{x} \, dx = \int \frac{y-1}{y} \, dy = 0$

and it should be blue sky all the way now.