(a) the stationary paths of the functional | S[y] = [d dx F(x,y,y', y″), y(a) = A, y(b) = B, satisfy the Euler-Lagrange equation ම‍ෙ d² OF dx2 ay" ;) d 'ƏF` dx dy' მყ OF + = 0, y(a)=A,_y(b) = B, Fy"|q = Fy" |₁ = 0. (b) Apply the result found in part (a) to the functional defined in equation (10.1) (page 219), with p = constant and the boundary conditions y(0) = y(L) = 0, to derive the associated Euler-Lagrange equation and show that its solution is y(x) = pg -x (L − x) (L² + xL — x²) . 24k - -