Past exam of the short options course of the University of Oxford / 2017 / 6 / b / i / Solution

Part (a)(ii) now givesIf $\lambda =0$, continuity makes $y^{\prime }$ identically zero. Thus $y$ is constant, and the boundary condition forces $y=0$, contradicting ${\int }_0^{\pi }{y}^2=1$. Hence