Show that the following differential equation $\displaystyle (4x + 2y + 1)dx + (3x + 2y + 1)dy = 0$ represents a family of hyperbolas having lines $\displaystyle x + y = 0$ and $\displaystyle 2x + y + 1 = 0$ as asymptotes.

EDIT:

As Danny rightly pointed out, the differential equation is actually:

$\displaystyle (4x + 3y + 1)dx + (3x + 2y + 1)dy = 0$