Déterminer les éléments propres des endomorphismes suivants :
1
\(E = \R[X]\) \(\Phi(P)(X) = X^2P''(X) + XP'(X)\).
2
\(E = \mathcal{C}^\infty(]0,+\infty[)\) \(\Phi(f)(x) = x^2f''(x) + xf'(x)\).
3
\(E = \mathcal{C}^\infty(]0,1[)\) \(\Phi(f)(x) = \sqrt{\frac {1-x}x}f'(x)\).