Laplace Technique to Find General Solution of Differential Equations without Initial Conditions

Authors: Adil Al-Rammahi

Abstract:

Laplace transformations have wide applications in engineering and sciences. All previous studies of modified Laplace transformations depend on differential equation with initial conditions. The purpose of our paper is to solve the linear differential equations (not initial value problem) and then find the general solution (not particular) via the Laplace transformations without needed any initial condition. The study involves both types of differential equations, ordinary and partial.

Keywords: Differential Equations, Laplace Transformations.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1337903

References:

[1] M.O. Bernard, M. Plapp, and J. Francois , Mean-Field Kinetic Lattice Gas Model of Electrochemical Cells, Physical Review E 68, (2003), (1- 14).
[2] J.S Moon,C. Athas, S.D. Soli, J.T. Drape and P.A. Beerel, Voltage- Pulse Driven Harmonic Resonant Rail Drivers for Low-Power Applications, IEEE Transaction on very large scale integration Systems (VLSI ), 11, OCT. , 2003, ( 5-12).
[3] K. Ogata, Modern Control Engineering, Prentice, Hall International Pub., 1984.
[4] A. Podlubny, Fractional Differential Equations, Academic Press, San Diego,1999.
[5] A. Sutradhar , H .P Glaucio , and L. J. Gray, Transient Heat Conduction in Homogenous and non Homogenous Materials by the Laplace Transform Galerkin Boundary Element Method, Eng. Boundary Elements 26, 2002 , (119-132).
[6] W.O. Xu, Boundary Conditions and Boundary Layers for a Multi- Dimensional Relaxation Model, J. Differential Equations, 197, 2004, (85–117).
[7] K.K. Salhotra, A Test Book of Electrical Engineering Mathematics, Katson Pub. House, 1998.
[8] F. Brauer and J.A. Nohel, Ordinary Differential Equations A First Course, Benjamin Pub. 2e, 1972.
[9] F. Iris, Schaum's Outlines of Theorems And Problems in Differential Equations, McGraw Hill Book Company , 1972.
[10] K. Kreiszig, Advanced Engineering Mathematics, Jhon Wiley and Sons Company, 1975.
[11] B.J.Y. Luka, Methods in Applied Mathematics, Basra University Press, 1998.
[12] G. Stephenson, Mathematical Methods for Science Students, Longman 2e, 1975.
[13] I.N. Sneddon, The Use of Integral Transforms , McGraw Hill Book Company, 1972 .
[14] C.R. Wylie, Advanced Engineering Mathematics, 4e, McGraw Hill Book Company, 1975.
[15] N.A. Hussein, Generalized New Methods of Laplace Transformations to Solve Linear Partial Differential Equations of Second Order with Constant Coefficients With or Without Conditions, M. SC. Thesis, College of Education, Kufa University, 2007.