Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Calculus of Variations Euler-lagrange Equation
Which of the following is an extremal of the functional \(I\left( y \right) = \int_{ - 1}^1 {\left( {{y^{'2}} - 2xy} \right)} \,dx\) that satisfies the boundary conditions y(-1) = -1 and y(1) = 1?
1
\(-\frac{x^3}{5}+\frac{6x}{5}\)
2
\(-\frac{x^5}{8}+\frac{9x}{8}\)
3
\(-\frac{x^3}{6}+\frac{7x}{6}\)
4
\(-\frac{x^3}{7}+\frac{8x}{7}\)
5
Question Not Attempted