# Exponential ODE Numerical Issues

I have an ODE such as the one below,

$$y"=a^{2}y$$

The analytical solution is clearly

$$y=C_{1}e^{ax} + C_{2}e^{-ax}$$

To apply boundary conditions $y(x=x_{1})=A$ and $y(x=x_{2})=B$, I recast into a matrix: