(a) the stationary paths of the functional b Slyl = dx F (x, y,y',y"), y(a) = A, y(b) = B, a satisfy the Euler-Lagrange equation d2 OF d OF OF da2 dy" dac ay' =0, y(a) = A, y(b) = B, Fy" = Fy =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 L (10 . 1) Elys = So dx ( Zky" - 9 plxy ) y(x) = pg (L-x) (L' +EL -22). 0 24k