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International Journal of Mathematics and Mathematical Sciences
Volume 9, Issue 2, Pages 405-408
http://dx.doi.org/10.1155/S0161171286000509
Research notes

An integral equation associated with linear homogeneous differential equations

Department of Mathematical Sciences, Clemson University, Clemson 29631, South Carolina, USA

Received 7 March 1985

Copyright © 1986 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Associated with each linear homogeneous differential equation y(n)=i=0n1ai(x)y(i) of order n on the real line, there is an equivalent integral equation f(x)=f(x0)+x0xh(u)du+x0x[x0uGn1(u,v)a0(v)f(v)dv]du which is satisfied by each solution f(x) of the differential equation.