The extremizer of the problem \(\rm min\left[\frac{1}{2}\int_{-1}^1[y'(x))^2+(y(x))^2]dx\right]\) subject to \(\rm y\in c^1[-1,1], \int_{-1}^1xy(x)dx=0\ and \ y(-1)=y(1)=1\) is
1
\(\rm \frac{e}{1+e^2}(e^x+e^{-x})+x^2-1\)
2
\(\rm \frac{e}{1+e^2}(e^x+e^{-x})+1-x^2\)
3
\(\rm \frac{e}{1+e^2}(e^x+e^{-x})\)
4
\(\rm \frac{e}{1+e^2}(e^x+e^{-x})+\sin (2\pi x)\)