# Parity of a simple linear differential equation's solution [duplicate]

Is it possible to solve this linear integral equation defined on $$[-a,a]$$? The boundary condition has two possibilities: 1) $$y(-a)=y(a)=b$$ and 2) $$-y(-a)=y(a)=c$$. $$y''(x)=\int_{-a}^{a}{ d x' \frac{y(x)-y(x')}{(x-x')^2} }$$ I think case 1) & 2) only have even and odd solution, respectively, because the operator is even and if we assume uniqueness for it's linear.

I feel the solution could be something simple. But I am not sure how to proceed.

• Obviously different equations. The other one doesn't have a differential term. Why duplicate? – xiaohuamao Feb 14 at 17:22