Second-Order Linear Equations · Superchallenge problem

For how many ordered pairs of integers $(b, c)$ with $1 \le b \le 20$ and $1 \le c \le 20$ does every solution of $y'' + by' + cy = 0$ satisfy $|y(t)| \le Ce^{-2t}$ for all $t \ge 0$, for some constant $C$ (which may depend on the solution)?