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^4y^(4)(t)+t^3y′′′(t)+t^2y′′(t)+ty′(t)+my(t)=0 where m is an integer and t ∈ 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,wherek∈N.