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{\bf HW1}
\begin{enumerate}
 \item 


Solve
$$
\min_{u(x)} \int_0^1 \left( u'^2 - \omega^2 u^2 \right) dx + 2 u(1), ~~ u(0) =0, 
$$
 \item 
Solve
$$
\min_{u(x), b} \int_0^b \left( u'^2 + 2 x \,u \right) dx  ~~ u(0) =0, ~~ u(b)= 0,
$$

 \item 
Solve
$$
\min_{u(x)} \int_0^b \left( u'^2 + a\, u\, u' + u\right) dx  ~~ u(0) =0.
$$
Explain the dependence of the solution on $a$
\end{enumerate}

\end{document}
