International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 2, Pages 405-408
Research notes

An integral equation associated with linear homogeneous differential equations

A. K. Bose

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

Received 7 March 1985

Copyright © 1986 A. K. Bose. 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.


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.