This was a test question that I got wrong and the professor did not explain it.
Given the second order equation Y''=-(Z^2)y, defined for 0<=x<=L.
a.) Verify that for any constants A and B, y=AsinZx+BcosZx.
b.) Find the value of Z, such that the solution satisfies the two conditions y(0)=0 and y(L)=0.
I got part A correct but had no clue what to do about part B.