ON THE RELATION BETWEEN DISTINCT PARTICULAR SOLUTIONS OF EQUATION Y'=SIGMA(I=0)N A(I)(X)Y(I)

There exists a relation (1.5) between any n + 2 distinct particular so lutions of the differential equation [GRAPHICS] In this paper, we show that when and only when n = 0, 1 and 2, this relation can be represen ted by the following form: PHI(n)(y1(x), y2(x), ..., y(n+2)(x)) = C, p rovided the form of this relation function PHI(n) depends only on n an d is independent of the coefficients of the equation. This result reve als interesting properties of these non-linear differential equations.