Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2021 / Paper 1 / 13 / a / iii / Solution

Combine the complementary function and particular solution:The boundary condition at zero gives $C_1+2/3=0$, while that at $\pi /2$ gives $C_2+1/3=0$. HenceThe two boundary conditions determine both constants uniquely; substitution at each endpoint gives zero.