Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Linear Integral Equations Fredholm and Volterra Integral Equation
Which of the following is the kernel of the boundary value problem \(\frac{d^2ϕ}{dx^2}+\lambda ϕ(x)\) = x with ϕ(0) = 0, ϕ'(1) = 0 is
1
K(x, ξ) = \(\begin{cases}x, x>\xi\\\xi, x<\xi\end{cases}\)
2
K(x, ξ) = \(\begin{cases}x, x<\xi\\\xi, x>\xi\end{cases}\)
3
K(x, ξ) = \(\begin{cases}x, x>\xi\\ 1, x<\xi\end{cases}\)
4
K(x, ξ) = \(\begin{cases}x, x>\xi\\0, x<\xi\end{cases}\)
5
Question Not Attempted