Consider the eigenvalue problem$$x^2 X″+2xX′+\lambda X=0,\ \ x \ \ \epsilon (\frac{2}{3},\frac{3}{2}), \ \ X′(\frac{2}{3})=0; \ \ \ X′(32)=0 \ \ \ \ \ (0)$$Assume $ \lambda \geq 0 $. Find all the eigenvalues and the corresponding eigenfunctions. Hint: as (1) is Euler equation, look for elementary solutions in the form $x^m$).