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- #1

\[

\frac{\partial F}{\partial u_i} - \frac{d}{dx}\left[\frac{\partial F}{\partial u_i'}\right] = 0

\]

From the E-L equations, I found

\begin{align*}

\frac{d}{dx}\left[2Au_1' + Bu_2'\right] &= 0\\

\frac{d}{dx}\left[2Cu_2' + Bu_1'\right] &= 0\\

2Au_1' + Bu_2' &= D\\

2Cu_2' + Bu_1' &= E

\end{align*}

Just a general question. Is this DE going to be extremely difficult to solve or is it relativily trivial?