I've used Euler-Lagrange and can't seem to get the right answer, please help if you can.

Determine the extremal for the functional

$\displaystyle \int_{0}^{1}(xy+y^2-2y^2y') dx$

with $\displaystyle y(0)=0, y(1)=2$

Using Euler-Lagrange I get,

$\displaystyle \frac{\partial f}{\partial y}+\frac{\mathrm{d}}{\mathrm{d} x}(\frac{\partial f}{\partial y'})=x+2y-4yy'+4yy'=x+2y=0$

but that isn't consistent with the given b.c.s

Please help!