Find the extremal for the following constrained CoV problem, involving two state variables and a constraint represented by a differential equation: J ¼ Z 1 0  y1  y2 2  dt s:t: dy1 dt ¼ y2 and boundary conditions as follows: y1ð0Þ ¼ 0; y2ð0Þ ¼ 0; y1ð1Þ ¼ free; y2ð1Þ ¼ free

a. Set up the augmented functional.

b. Identify via the EulereLagrange equations the conditions for the solution of the problem.

c. Plot the numerical solutions for the two state variables.