Find the extremal in the following isoperimetric constrained problem: min J Z 1 0 1 2

Find the extremal in the following isoperimetric constrained problem: min J ¼ Z 1 0 1 2  y2 1 þ y2 2 þ 2y' 1y' 2  dt s:t: Z 1 0 y2 2dt ¼ 8 ðIsoperimetric constraintÞ Exe and y1ð0Þ ¼ 0; y2ð0Þ ¼ 0; y1ð1Þ ¼ free; y2ð1Þ ¼ free