The solution of the differential equation
$\frac{d^3 y}{d x^3}-5.5 \frac{d^2 y}{d x^2}+9.5 \frac{d y}{d x}-5 y=0$
is expressed as $y=C_1 e^{2.5 x}+C_2 e^{\alpha x}+C_3 e^{\beta x}$, where $C_1, C_2, C_3, \alpha$, and $\beta$ are constants, with $\alpha$ and $\beta$ being distinct and not equal to $2.5.$ Which of the following options is correct for the values of $\alpha$ and $\beta$ ?
- $1$ and $2$
- $-1$ and $-2$
- $2$ and $3$
- $-2$ and $-3$