Solution
= Solution
The boundary term $[f_{y'}\eta]_a^b$ vanishes, so stationarity and the <fundamental lemma of the calculus of variations> give the <Euler-Lagrange equation>
$$
\boxed{f_y-\frac{d}{dx}f_{y'}=0.}
$$
= Solution
The boundary term $[f_{y'}\eta]_a^b$ vanishes, so stationarity and the <fundamental lemma of the calculus of variations> give the <Euler-Lagrange equation>
$$
\boxed{f_y-\frac{d}{dx}f_{y'}=0.}
$$