Find the eigenfunctions of the Sturm-Liouville problem y" + y = 0, y(0) = 0, y' (L) = 0, and make the set an orthonormal set of eigenfunctions.

Show that A=[0110] has no real eigenvalues.

Consider the eigenvalue problem           y"+2y'+(lambda)y=0;     y(0)=0,       y'(1)=0. Show that the eigenvalues are all positive and that the nth positive eigenvalue is (lambda)n= an^2+1 with associated eigenfunction yn(x)= e^-x sin(anx) where anx is the nth positive root of tanz=z

I try to use the eigenvalue to find eigenvector, and I've already found the relation between x and y. I can substitute x=1 and get y=-i, but the solution provided is substituting x=-1 and get  y=i. There is a problem, how can I know which value of x should I choose?