Math 6420 • PDE

\begin{enumerate}
\item[(a)] Find the extended operator for the boundary value problem (BVP):
\begin{equation}
  y''-y=f(x),\qquad ay(0)+y'(0)=0,\qquad y'(1)=a.
\end{equation}
\item[(b)] Solve the differential equation in the sense of distributions:
\begin{equation}
  xu'=\delta(4x^2-1),\qquad x\in[-1,1],\qquad x(-1)=1,\qquad x(1)=0.
\end{equation}
Discuss why the first order differential equation satisfies two boundary conditions.
\end{enumerate}