Which family of curves has the differential equation $\frac{dy}{dx} = -2y$?

Explanation

1. 01

   For $y = Ae^{-2x}$, $\frac{dy}{dx} = -2Ae^{-2x} = -2y$, for every $A$.

2. 02

   $Ae^{2x}$ gives $+2y$, and $-2x + A$ gives $-2$, not $-2y$.