Final answer:
To determine the eigenvalues of the problem with the given boundary conditions, we need to solve the differential equation involving the differential operator C = d/dy. The eigenvalues will depend on the boundary conditions and the domain of the problem.
Step-by-step explanation:
The eigenvalues of the problem with the boundary conditions Cy + λy = 0, y(0) = y(L) = 0 can be determined by solving the differential equation. In this case, the differential operator C is defined as C = d/dy. So, we need to solve the equation C(y) + λy = 0.
Substituting C = d/dy into the equation gives us d^2y/dy^2 + λy = 0. This is a second-order linear ordinary differential equation. The solutions to this equation are given by the characteristic equation: r^2 + λ = 0.
By solving the characteristic equation, we can find the eigenvalues λ of the problem. The eigenvalues will depend on the boundary conditions and the domain of the problem.