An integral equation associated with linear homogeneous differential equations (Q1077603)

Summary: Associated with each linear homogeneous differential equation \(y^{(n)}=\sum^{n-1}_{i=0}a_ i(x)y^{(i)}\) of order n on the real line, there is an equivalent integral equation \[ f(x)=f(x_ 0)+\int^{x}_{x_ 0}h(u)du+\int^{x}_{x_ 0}[\int^{u}_{x_ 0}G_{n-1}(u,v)a_ 0(v)f(v)dv]du \] which is satisfied by each solution f(x) of the differential equation.