Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Ordinary Differential Equations Green’s Function
The Green's function G(x, x') for the equation \(\rm\frac{d^2y(x)}{d x^2}\) +y=0, with the boundary values y(0) = 0 and y(1) = 0, is
1
G(x, x') = \(\begin{cases}\frac{1}{2} \rm x\left(1−x'\right), & 0<\rm x
2
G(x, x') = \(\begin{cases}\rm x\left(x'−1\right), & 0<\rm x
3
G(x, x') = \(\begin{cases}−\frac{1}{2} \rm x\left(1−x'\right), & 0<\rm x
4
G(x, x') = \(\begin{cases}\rm x\left(x'−1\right), & 0<\rm x