Find the minimum value taken by the integral expression

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Homework Statement

find the minimum value taken by the integral expression

integral from 0 to pi/2 [(y')^2]-(y^2)+2xy dx
y(0)=0
y(pi/2)=pi/2

The Attempt at a Solution

using euler lagrange
d/dx(2y')-(-2y+2x)=0
2y''+2y-2x=0
from here I'm stuck

 

[Dick]

Now it's just an ordinary differential equation, y''+y=x. To get the most general solution solve the homogeneous part y''+y=0 and then look for a particular solution. Then use the boundary values to fix the constants.