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

question 40

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

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