Find Three Positive Values Of $\lambda$ For Which the Differential Equation $\left( 1 - x ^ { 2 } \right) y ^ { \prime \prime } - 2 x y ^ { \prime } + \lambda y = 0$

Multiple Choice

Find three positive values of $\lambda$ for which the differential equation $\left( 1 - x ^ { 2 } \right) y ^ { \prime \prime } - 2 x y ^ { \prime } + \lambda y = 0$ has polynomial solutions.

A) 2, 6, 12
B) 1, 2, 3
C) 1, 4, 9
D) 2, 4, 6
E) 2, 6, 10