Discussions are presented by Morita and Sato on the problem of obtaining the particular solution of an inhomogeneous differential equation with polynomial coefficients in terms of the Green's function. In the present paper, solution is given without using the Green's function, on...
Open access
Research Article10.9734/jamcs/2023/v38i31751
It is shown that the index law of the Riemann-Liouville fractional derivative is recovered when nonstandard analysis is applied, and then the solutions of Euler’s differential equation are obtained in nonstandard analysis, where infinitesimal number appears. They are given in the...
Open access
Research Article10.9734/jamcs/2021/v36i130329
A linear differential equation with polynomial coefficients is studied. In the preceding study given in J. Adv. Math. Comput. Sci. 2018; 28 (3) 1-15, the equation is expressed in terms of blocks of classified terms, and the full solutions near the origin are presented for the dif...
Open access
Research Article10.9734/JAMCS/2018/45273
The particular solutions of inhomogeneous differential equations with polynomial coefficients in terms of the Green's function are obtained in the framework of the AC-Laplace transform, that is the Laplace transform supplemented by its analytic continuation. In particular, discus...
Open access
Research Article10.9734/JAMCS/2018/43059
A linear differential equation with polynomial coefficients, which is expressed by is studied, where ak,m are constants. In the present study, the lefthand side of the equation is rewritten where and each of is called a block of classified terms in Lu(t). The solution is...
Open access
Research Article10.9734/JAMCS/2018/43000