# Linear homogeneous second order ODE with a non-constant coefficient

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.