Teaching CSIR NET Mock Test Series Mathematical Science Ordinary Differential Equations Green’s Function
Consider the boundary value problem (BVP)
(e-5xy')' + 6e-5xy = -f(x), 0 < x < ln 2,
y(0) = 0, y(ln 2) = 0.
If
\(\rm G(x, \xi)=\left\{\begin{matrix}(e^{3x}+Be^{2x})(Ce^{2\xi}+De^{3\xi}),&0\le \xi\le x,\\\ (e^{3\xi}+Be^{2\xi})(Ce^{2x}+De^{3x}),&x \le \xi \le \rm ln\:2,\end{matrix}\right.\)
(Green’s function) is such that \(\rm \int_0^{ln\:2}G(x, \xi)f(\xi)d\xi\) is the solution of the BVP, then the values of B, C and D are
1
B = -2, C = -1, D = 1
2
B = -2, C = 1, D = -1
3
B = 2, C = 1, D = 1
4
B = 2, C = -1, D = -1