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Find the eigenfunctions for the following boundary value problem. \[ x^{2} y^{\prime \prime}-19 x y^{\prime}+(100+\lambda) y=0, \quad y\left(e^{-1}\right)=0, y(1)=0 . \] In the eigenfunction take the arbitrary constant (either \( c_{1} \) or \( c_{2} \) ) from the general solution to be 1. Enter your answer as a symbolic function of \( x, n \), as in these Do not include ' \( y= \) ' in your answer. examples

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