Mathematical Science Calculus of Variations Euler-lagrange Equation

If \(J[y]=\int_1^2\left(y^{\prime 2}+2 y y^{\prime}+y^2\right) d x\), y(1) = 1 and y(2) is arbitrary then the extremal is

1
\(e^{x-1}\)
2
\(e^{x+1}\)
3
\(e^{1-x}\)
4
\(e^{-x-1}\)
5
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