Associated with each linear homogeneous differential equation y ( n ) = ∑ i = 0 n − 1 a i ( x ) y ( i ) of order n on the real line, there is an equivalent integral equation f ( x ) = f ( x 0 ) + ∫ x 0 x h ( u ) d u + ∫ x 0 x [ ∫ x 0 u G n − 1 ( u , v ) a 0 ( v ) f ( v ) d v ] d u which is satisfied by each solution f ( x ) of the differential equation.