Chapter 11.4, Problem 13E

To determine

Whether $\lambda =0$ is an eigenvalue of the boundary value problem $\frac{d}{dx}\left[r\left(x\right)y^{\prime }\right]+\lambda p\left(x\right)y=0,y^{\prime }\left(a\right)=0,y^{\prime }\left(b\right)=0$.