Calculus of Variation

Find the boundary value problems satisfied by the function y1 and y2 if the vector value function Y= (y1, y2) is a local extremum for the functional J ( Y ) = y1yz + 3y2yi + t?(y2 - y1) dx, y1(0) = a, y1(1) = b, y2(0) = c, y2(1) = d. Finding closed form algebraic formulas for y1 and y2 may not be possible, but how much can you say about these functions