International Journal of Mathematics and Mathematical Sciences 
Volume 9 (1986), Issue 2, Pages 405-408
doi:10.1155/S0161171286000509
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

Abstract

Associated with each linear homogeneous differential equation y(n)=∑i=0n−1ai(x)y(i) of order n on the real line, there is an equivalent integral equation f(x)=f(x0)+∫x0xh(u)du+∫x0x[∫x0uGn−1(u,v)a0(v)f(v)dv]du which is satisfied by each solution f(x) of the differential equation.