The positive values of \(\lambda\) for which the equation y"(x) + \(\lambda\)2y(x) = 0 has non - trivial solution satisfying y(0) = y(π) and y'(0) = y'(π) are 

1
λ =\(\frac{2 n+1}{2}\), n = 1, 2, ...
2
λ= 2n, n = 1, 2,...
3
λ = n, n = 1, 2,...
4
λ= 2n - 1, n = 1,2,....
5
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