How do I solve this difference equation

How do I solve this difference equation

How do I solve this difference equation
$$-\epsilon\delta^2Y_i+aD^-Y_i=0,\;\; 1 \leq i\leq N-1,$$ with
$\delta^2V_i=(D^+-D^-)V_i/\bar h_i$, $D^+V_i=(V_{i+1}-V_i)/h_{i+1}$,
$D^-V_i=(V_i-V_{i-1})/h_i$ and $\bar h_i=(h_{i+1}+h_i)/2$. The mesh is
defined as
$$ h_i = \left\{ \begin{array}{lr} h_1 & \mbox{for}\; 0<i\leq N/2,\\ h_2 &
\mbox{for}\; N/2<i\leq N \end{array} \right. $$ My challenge is how to
manipulate $h$'s since it depends on the interval.