Could you help me the with part a) ? I tried to derive the Euler Lagrange equation but I'm having trouble. Also shouldn't it hold for the whole interval [0,2]?

4. Consider the functional 4 J (y) = A [(y'2 +y2)(y - If - 5:93 + 2W2] div, y(0) = 0: 31(2) = e, where y is a piecewise smooth function. (a) Find the corresponding EulerLagrange dierential equation and nd out at what points in [0, 2] it must hold. (b) Show that y = :1: and y 2 ae'\" are solutions of the equation found in part (a). (c) Find all possible corner points for the extremals of the functional J. ((1) Find a possible extremal for our