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For what values of a (if any) does the boundary value problem x'' + ax' =...

For what values of a (if any) does the boundary value problem
x'' + ax' = 0, x(0) = 0, x(π) = 0
have nontrivial (i.e. nonzero) solutions

Hint: In order to solve, divide the problem into three cases
1. If a > 0. In this case let a = b^2. 2. If a < 0. In this case let a = −b^2. 3. If a = 0.

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