Green's Functions and Infinite Products by Yuri A. Melnikov

Author:Yuri A. Melnikov
Language: eng
Format: epub
Publisher: Birkhäuser Boston, Boston

as well as

This reduces the equation in (4.49) to

(4.50)

The relations in (4.46) and (4.50) represent a system of linear algebraic equations in and . The system is well posed (has a unique solution) because the determinant of its coefficient matrix is the Wronskian

for the fundamental set of solutions y 1(x) and y 2(x).

Solving the system in (4.46) and (4.50), we obtain

Straightforward integration of the above expressions yields

and

where H 1 and H 2 are arbitrary constants of integration.

Upon substituting these expressions for C 1(x) and C 2(x) into (4.44), we obtain the general solution of the equation in (4.41) in the form

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