Please find the solution to the corresponding EulerLagrange

Please find the solution to the corresponding Euler-Lagrange equation subject to the stated boundary conditions:

Please find the solution to the corresponding Euler-Lagrange equation subject to the stated boundary conditions: Integrate e^3x[(y?)^2 + 2y]dx; y(0) = 0 y(1) = ½ , with Constraint integrate 2ydx between the limits 0 to 1 = 1/6