I would like to know how one solves Sturm-Liouville problems on $(0,\infty)$ NUMERICALLY for the eigenvalues that are of the form

$$-f''(x)+\frac{1}{\sinh(x)^2}f(x)=\lambda f(x).$$

So even if there is a closed form solution to this problem, I would like to know how to treat singularities like this one with a computer. I also do not want to use programs, I am just interested in how to do this "by hand with a computer".