Find the extremal for the following CoV problem, involving two independent functions: J Z p 4

Find the extremal for the following CoV problem, involving two independent functions: J ¼ Z p 4 0  y2 1 þ y0 1y0 2 þ y2 2  dt s:t: y1ð0Þ ¼ 1; y2ð0Þ ¼ 3=2 and y1 p 4 ¼ 2; y2 p 4 ¼ free Set up, to solve the problem, the problem the necessary transversality condition.