Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Linear Integral Equations Resolvent Kernel
Which of the following is the resolvent kernel for the integral equation \(\phi(x)=x+\int_{-1}^{0} (1+x)(1-\xi)\phi(ξ) d ξ\)
1
\(\frac{2}{3+2\lambda}\)(1+x)(1−ξ)
2
\(\frac{1}{3+\lambda}\)(1+x)(1−ξ)
3
\(\frac{2}{2-\lambda}\)(1+x)(1+ξ)
4
\(\frac{3}{3-2\lambda}\)(1+x)(1−ξ)
5
Question Not Attempted