Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Linear Integral Equations Characteristic Numbers and Eigenfunctions
For the homogeneous Fredholm integral equation \(\phi(x)=λ \int_{0}^{1} e^{x+3t} \phi(t) d t\), a non-trivial solution exists, when λ has the value
1
\(\lambda=\frac{2}{e-1}\)
2
\(\lambda=\frac{4}{e^4+1}\)
3
\(\lambda=\frac{4}{e^4-1}\)
4
\(\lambda=\frac{2}{e^4-1}\)
5
Question Not Attempted