The Solution of the Eigenvalue Problem $\left( 1 - x ^ { 2 } \right) y ^ { \prime \prime } - 2 x y ^ { \prime } + \lambda y = 0$

question 34

Multiple Choice

The solution of the eigenvalue problem $\left( 1 - x ^ { 2 } \right) y ^ { \prime \prime } - 2 x y ^ { \prime } + \lambda y = 0$ where $y$ is bounded on $[ - 1,1 ]$ , is

• A) \(\lambda = n , y = P _ { n } ( x ) , n = 1,2,3 ,\)
• B) \(\lambda = n - 1 , y = P _ { n } ( x ) , n = 1,2,3 , \ldots\)
• C) \(\lambda = n + 1 , y = P _ { n } ( x ) , n = 1,2,3 , \ldots\)
• D) \(\lambda = n ^ { 2 } , y = P _ { n } ( x ) , n = 1,2,3 , .\)
• E) \(\lambda = n ( n + 1 ) , y = P _ { n } ( x ) , n = 1,2,3 , \ldots\)

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