Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Linear Integral Equations Fredholm and Volterra Integral Equation
The integral equation of the initial value problem ϕ''(x) + λϕ(x) = F(x) with ϕ(0) = 1 and ϕ'(0) = 0 is
1
ϕ(x) = x + \(\int_0^x(x-\xi)\{F(\xi)-\lambdaϕ(\xi)\}d\xi\)
2
ϕ(x) = 1 +\(\int_0^x(x-\xi)\{F(\xi)-\lambdaϕ(\xi)\}d\xi\)
3
ϕ(x) = \(\int_0^x(x-\xi)\{F(\xi)-\lambdaϕ(\xi)\}d\xi\)
4
ϕ(x) = x +\(\int_0^x(x+\xi)\{F(\xi)-\lambdaϕ(\xi)\}d\xi\)
5
Question Not Attempted