Linear Second Order ODE/y'' - y' - 6 y = exp -x

Theorem
The second order ODE:
 * $(1): \quad y'' - y - 6 y = e^{-x}$

has the general solution:
 * $y = C_1 e^{3 x} + C_2 e^{-2 x} - \dfrac {e^{-x} } 4$