# How do you find and classify the critical points of this differential equation dx/dt = 2x + 4y + 4?

Critical Points occur when the first derivative vanishes, ie when $\frac{\mathrm{dx}}{\mathrm{dt}} = 0$ which requires that
$2 x + 4 y + 4 = 0$
ie along the curve $x + 2 y + 2 = 0$