Generalized Solutions of Ordinary Differential Equations Related to the Chebyshev Polynomial of the Second Kind

Abstract

In this work, we employed the Laplace transform of right-sided distributions in conjunction with the power series method to obtain distributional solutions to the modified Bessel equation and its related equation, whose coefficients contain the parameters (Formula presented.) and (Formula presented.). We demonstrated that the solutions can be expressed as finite linear combinations of the Dirac delta function and its derivatives, with the specific form depending on the values of (Formula presented.) and (Formula presented.).