How can I solve the ODE with boundary conditions? I have solved it without boundary conditions. I have no idea with such boundary conditions.
ODE:
$${\partial ^2 Y(X) \over \partial ^2 X} = \beta Y(X)$$
Boundary Conditions：
$${\partial \ln Y(X) \over \partial X} = \begin{cases} a < 0,X = k \\[5pt] b , X = 0 \\[5pt] c > 0,X = - k \end{cases} $$
where $a,b,c \in \mathbb{R}$ are given and $X$, $Y$ and $\beta$ are unkown.