Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1997. Sectio Mathematicae. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 24)

GRYTCZUK, K., General solution of the differential equation ...

General solution of the differential equation y" (x)-(y' (x))

2 +x

2 e

v(x

) = 0 119 Integrating the last equality with respect to x we obtain (1

0> J^)

dx = ~ u

x+cix + c On the other hand it easy to see that (id (_J_Y

=iM and consequently by (10) and (11) it follows that and we have 1 y(x) = In z(x) = -In (^z

4 + Ax + B J = - In W(x) where A = —C\, B = -C

2. The proof of the theorem is complete. References [1] S. RABINOWITZ, Index to Mathematical Problems, Westford, Massachusetts, USA, 1992. INSTITUTE OF MATHEMATICS TECHNICAL UNIVERSITY ZIELONA GORA, UL. PODGORNA 50 POLAND