I am having problem on solving ODE

$y'' - \Big( \frac{b^2}{c^2} + \frac{b}{c^2}\cdot \mu(x)\Big)y = 0$,

where $\mu(x) \geq 0$ for all $x$, $b$ and $c$ are constants and $c > 0$. I don't really come up with a function that satisfies this equation to start and I cannot use power series due to $\mu(x)$.

Does anyone can help me on this?

April 18: $y$ is a function of $x$, i.e. $y(x)$, if I did not make myself clear.


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