  We consider the number of roots of linear combinations of a system of $n$
orthogonal eigenfunctions of a Sturm-Liouville initial value problem with
i.i.d. standard Gaussian coefficients. We prove that its distribution inherits
the asymptotic behavior of the number of roots of Quall's random trigonometric
polynomials. This result can be thought as a robustness result for the central
limit theorem for the number of roots of Quall's random trigonometric
polynomials in the sense that small uniform perturbations of sines and cosines
do not change the limit distribution.
