Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1993. Sectio Mathematicae. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 21)

Krystyna Grytczuk: Effective integrability of the differenctial equation ...

KRYSTYNA GRYTCZUK EFFECTIVE INTEGRABILITY OF THE DIFFERENCTIAL EQUATION P

0 (*)/"> + P

x (x)y™ +...

+P

h (x)y = 0 ABSTRACT: In the paper [1] was proved that the functions y = s

0

i uf

y i = 1,2,...,« are the solutions of special form of differenctial equation (1) P

0 (x)/

n

) + P

x (x)/"-* +--+P

n (x)y = 0 This result is a generalization our recently result given in [2] for the case n- 2. The purpose of this paper is to give a necessary and sufficient condition for the function n (2) y

0 = J^s

o

kui k=

1 to be a particular solution of (1) and also to give a necessary and sufficient condition for the functions y

k - s

o k a

k for k = 1,2,...,« to be the particular solutions of (1). We note that Theorem B given in [1] follows easily from our results. We prove the follwing: 95