On the generalized solutions of a certain fourth order Euler equations

In this paper, using Laplace transform technique, we propose the generalized solutions of the fourth order Euler differential equations t(4)y((4)) (t) + t(3)y''' (t) + t(2)y '' (t) + ty' (t) + my (t) = 0, where m is an integer and t is an element of R. We find types of solutions depend on the values of m. Precisely, we have a distributional solution for m = -k(4) - 5k(3) - 9k(2) - 4k and a weak solution for m = -k(4) + 5k(3) - 9k(2) + 4k, where k is an element of N. (C) 2017 All rights reserved.