The differential equation of the following equation $y=ae^{2x} +be^{-3 x} +ce^{x}$

Question

$(a)\;\frac{7d^3 y}{dx^3}-\frac{7d^2y}{dx^2}+y=0 \\ (b)\;\frac{d^3 y}{dx^3}-7 \frac{d^2y}{dx^2}+6 \frac{d^2y}{dx^2}+y=0 \\ (c)\;\frac{d^3y}{dx^3}-\frac{7dy}{dx}+6y=0 \\ (d)\;\frac{d^2y}{dx^2}-6\frac{dy}{dx}+7=0$