Solution of piecewise second order linear difference equatio.

Solution of piecewise second order linear difference equatio.

I am trying to solve
$$-\dfrac{1}{h_{i+1}}Y_{i+1}-(\dfrac{1}{h_{i+1}}-\dfrac{1}{h_{i}}-(h_{i+1}+1)\dfrac{a}{2\epsilon})Y_{i}+(1-(h_{i+1}+1)\dfrac{a}{2\epsilon})Y_{i-1}=0,$$
where $Y_0$ and $Y_N$ are given.
The solution can be found by substituting $Y_i=Aw^i$ which results in an
quadratic equation from which $w$ is found. My problem I need a solution
for values $1\leq i\leq N/2-1$, $i=N/2$ and $N/2+1\leq i\leq N-1$. If the
problem was to find the solution for $1\leq i\leq N-1$, then I would not
have problems.
The value of $h$ for $1\leq i\leq N/2-1$ is $h_1$ and for $1\leq i\leq
N-1$, it's $h_2$