I have a question about a boundary value problem. It may sort of look intuitive at first, but it's sort of strange for me.
$$ BC: y(0) = 0, \ y(1) +y'(1) = 0\\ y''(x)+\lambda y(x) = 0 $$
So I solved the differential equation and got the general solution as: $$ y = c_1 cos(\sqrt\lambda x) + c_2sin(\sqrt\lambda x) $$ Applied the first boundary condition and got that: $$c_1 = 0$$
Then I applied the second boundary condition and got: $$ c_2(sin(\sqrt\lambda) + \sqrt\lambda cos(\sqrt\lambda )) = 0 $$
The only thing I could really say is that either: $$ c_2 = 0 $$ or $$ sin(\sqrt\lambda) + \sqrt\lambda cos(\sqrt\lambda ) = 0 $$
The problem is, I can't really see how to find the eigenvalues for this problem. It doesn't look very obvious to me, any sort of hints?