Which of the Following Differential Equations Are in Self-Adjoint Form $r ( x ) y ^ { \prime \prime } + r ^ { \prime } ( x ) y ^ { \prime } + \lambda y = 0$

question 36

Multiple Choice

Which of the following differential equations are in self-adjoint form? Select all that apply.

• A) \(r ( x ) y ^ { \prime \prime } + r ^ { \prime } ( x ) y ^ { \prime } + \lambda y = 0\)
• B) \(y ^ { \prime \prime } + y ^ { \prime } + \lambda y = 0\)
• C) \(\left( 1 - x ^ { 2 } \right) y ^ { \prime \prime } - 2 x y ^ { \prime } + \lambda y = 0\)
• D) \(y ^ { \prime \prime } + \lambda y = 0\)
• E) \(x ^ { 2 } y ^ { \prime \prime } + x y ^ { \prime } + \left( x ^ { 2 } - n ^ { 2 } \right) y = 0\)

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