Question

Need help with b)

In this problem we will examine the Green's function method for ordinary DE's in a somewhat more general way than presented in the lectures - although you can follow the logic in the lecture notes closely when doing a) and b). Consider the differential equation with specified boundary conditions (a) y(b)-0 We assume that two linearly independent solutions, yı() and y2(x), of the homogeneous equation are known, and that y(a)y2(b) 0 a) Show that the Green's function is where W(z)z)2(z) y2(2)(z) is the Wronskian. (Make sure to keep track of which variables are r's and which are z's...) b) Proceed by showing that the full solution of the DE can be written as

Answer 1

s N. we hove VA

thou 2- ni (z) atn 0