Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Calculus of Variations Euler-lagrange Equation
The extremal of the functional
\( J(y)=\int_0^1\left[2\left(y^{\prime}\right)^2+x y\right] d x, \) y(0) = 0, y(1) = 1, y ∈ C2[0, 1]
1
\(y=\frac{x^2}{12}+\frac{11 x}{12}\)
2
\(y=\frac{x^3}{3}+\frac{2 x^2}{3}\)
3
\(y=\frac{x^2}{7}+\frac{6 x}{7}\)
4
\(y=\frac{x^3}{24}+\frac{23 x}{24}\)
5
Question Not Attempted