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.