This is a problem from the book Partial Differential Equations by Walter.A.Strauss.
Consider the eigen value problem with Robin Boundary Conditions at both ends:
a)Show that $\lambda=0$ is an eigenvalue if and only if $a_0+a_1=-a_0a_1 l$
b)Find the eigen functions corresponding to the zero eigenvalue
(Hint: First solve ODE for X(x).The solutions are not sines or cosines).
I was able to do part a) if $\lambda=0$ then $a_0+a_1=-a_0a_1 l$.
But the rest of part a) and part b) I am unable to do.
Can someone please help me to finish this problem