Math 6420 • PDE

\begin{enumerate}
\item[(a)] Write down the set of linear equations which if solved give the Green's function
for the operator \(Lu=d^3u/dx^3\) on the interval \([0,1]\) with boundary conditions
\(u(0)=u'(0)=u(1)=0\). (There is no need to explicitly solve these equations).

\item[(b)] Letting \(G(x,y)\) denote the Green's function which solves (a), and using a particular
solution of \(d^3u/dx^3=0\), find the general solution to \(d^3u/dx^3=f(x)\) on the interval
\([0,1]\) with boundary conditions \(u(0)=u'(0)=0\) and \(u(1)=1\).
\end{enumerate}