Question: find the eigenvalues and eigenfunctions of
$$y'' + \lambda y = 0, $$
with boundary conditions $y(0) + y'(0) = 0$ and $y(1)=0$.
I think I may be making an incredibly trivial error here, yet can't seem to spot it.
Assuming $\lambda=0$, we get $y(x) = c_1 + c_2\,x$. Differentiating, and using the boundary conditions, $(I)$ get $(2)$ equations, both of which say $c_1 + c_2 = 0$, i.e. $c_1 = -c_2$.
Having checked the answers, I have done it all right, except when using the boundary conditions, the answer I should get seems to be $y(x)= 1-x $, implying $c_1 = 1$, $c_2 = -1 $
Just wondering if another brain might be able to pick up my error !