计算 $n$ 阶行列式

$$
D_n=\left|\begin{array}{cccccc}
\lambda & x & x & x & \cdots & x \\
y & \alpha & \beta & \beta & \cdots & \beta \\
y & \beta & \alpha & \beta & \cdots & \beta \\
\vdots & \vdots & \vdots & \vdots & & \vdots \\
y & \beta & \beta & \beta & \cdots & \alpha
\end{array}\right| .
$$