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.

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