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**Opalg** The equation $\displaystyle (y^{2}-1)\frac{d^{2}\psi}{ dy^{2}}+y\frac{d\psi}{dy}+\left ( \frac{20}{y^{2 }} + \lambda\right )\psi =0$ has eigenfunctions $\displaystyle \psi(y) = y^5$ and $\displaystyle \psi(y) = y^{-4}$, with corresponding eigenvalues $\displaystyle \lambda = -25$ and $\displaystyle \lambda=-16$ (see my comment #3 above).

thanks, can you write please first steps of your solution, in the article he got a little different answer...

$\displaystyle \lambda_{1} =-16,

\lambda_{2} =-4$