The problem is y'' + λy = 0 with y'(0) = 0 and y(L) = 0 We need to check for λ < 0, λ = 0, and λ > 0, by substituting λ = u^2, λ = -u^2, and solving for the non-trivial solution. The answer is y(x) = cos((2n - 1) π x / 2L) .... n = 1, 2, 3 .... I added spaces to make the symbols easier to read. I just need some help getting to the answer. Thanks a lot!!