I saw this question:
Find the Green function for the problem:
$$y''(x)+y(x) = h(x)$$ $$y(0)=y(\pi), y'(0)=y'(\pi)$$
My attempt:
First I should consider the homogeneous case, in that case:
$y''=0 \Longrightarrow y=c_1x+c_2$
$y(0)=y(\pi) \Longrightarrow c_2 = c_1\pi+c_2 \Longrightarrow c_1=0$
So for the first boundary condition I have: $y_1=c_2$ $??$
$y'(0)=y'(\pi) \Longrightarrow c_1=c_1$
It seems like from the second boundary condition I do not get any information about $y_2$ which would help me to calculate the Wronskian and so on. Also I am not sure $y_1$.
Could you please help me?