Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Calculus of Variations Euler-lagrange Equation
Consider the functional
\(J(y)=y^2(1)+\int _0^1 y^{\prime 2}(x) d x\) y(0) = 1, where y ∈ C2([0, 1]) If y extremizes J, then
1
\(y(x)=1-\frac{1}{2} x^2\)
2
\(y(x)=1-\frac{1}{2} x\)
3
\(y(x)=1+\frac{1}{2} x\)
4
\(y(x)=1+\frac{1}{2} x^2\)
5
Question Not Attempted