Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have the following Sturm-Liouville problem: $$\frac{d^2 y}{dx^2}+\lambda x^2y=0,$$ where $y(0)=0$ and $y(1)=0$.

I have solved this using MAPLE and found the exact solution to be: $$y(x)=c_1\sqrt{x}J_\frac{1}{4}(\frac{1}{2}\sqrt{\lambda}x^2)+c_2\sqrt{x}J_\frac{1}{4}(\frac{1}{2}\sqrt{\lambda}x^2).$$ Where J is the Bessel function.

I am told to use the "BesselJZeros" command in MAPLE to find the smallest eigenvalue, any help much appreciated.

share|improve this question

1 Answer 1

up vote 0 down vote accepted

The first term vanishes at the origin but the second, which should read $c_2\sqrt{x}J_{-1/4}(\sqrt{\lambda}x^2/2)$, has a nonzero limit there. So the first boundary condition requires $c_2=0$. Then the second boundary condition says $J_{-1/4}(\sqrt{\lambda}/2)=0$ so you'll need the first zero of $J_{1/4}$.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.