If $y=e^{2 t}$ is a solution to the differential equation $$\frac{d^2y}{dt^2} - 6 \frac{dy}{dt} + ky = 0,$$ find the value of the constant $k$ and the general solution to this equation.

$k =$
$y =$
(Use constants A, B, etc., for any constants in your solution formula.)