Math 6420 • PDE

\begin{enumerate}
\item[(a)] Find the Green's function for the BVP:
\begin{equation}
  -u''=f;\qquad 0<x<1,\qquad u(0)=0,\qquad \int_0^1 xu'(x)\,dx=\gamma.
\end{equation}
\item[(b)] Find the modified Green's function for the BVP:
\begin{equation}
  -u''=f;\qquad 0<x<1,\qquad u(0)=u(1),\qquad u'(0)=u'(1).
\end{equation}
\end{enumerate}