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(See Solution) Consider the problem: x^2 y^prime \prime=λ(x y^prime-y), y(1)=0, y(2)=0 . Note that λ appears as a coefficient of y as well as of

Question: Consider the problem:

\[x^{2} y^{\prime \prime}=\lambda\left(x y^{\prime}-y\right), y(1)=0, y(2)=0 .\]

Note that \(\lambda\) appears as a coefficient of \(y\) as well as of \(y\) itself. (In an extended definition of self-adjointness which also applies to this type of problem, it can be shown that this problem is not self-adjoint). Show that the problem has eigenvalues, but that none of them are real. This illustrates that in general non self-adjointness problems may have eigenvalues that are not real.

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