A general solution of some linear partial differential equations via two integral transforms

Document Type : Research Paper


College of Education for Pure Sciences/ Ibn Al- Haithem, University of Baghdad, Baghdad, Iraq


In this paper, a new analytical method is introduced to find the general solution of linear partial differential equations. In this method, each Laplace transform (LT) and Sumudu transform (ST) is used independently along with canonical coordinates. The strength of this method is that it is easy to implement and does not require initial conditions.


[1] A. Al Rammahi, Laplace technique to find general solution of differential equations without initial conditions, Int. J. Math. Comput. Phys. Quantum Engin. 8(11) (2014).
[2] R. Chauhan, N. Kumar and S. Aggarwal, Dualities between Laplace Carson transform and some useful integral transforms, Int. J. Innov. Technol. Exploring Engin. 8(12) (2019).
[3] R.V. Churchill, J.W. Brown and R.F. Verhey, Complex Variable and Applications, Third Ed., Mc Graw-Hill Kogakusha, Ltd., Tokyo, 1974.
[4] T.M. Elzaki, S.M. Elzaki and E. M.A. Hilal, Elzaki and Sumudu transforms for solving some differential equations, Glob. J. Pure Appl. Math. 8(2) (2012).
[5] A.K. Hayder, A method for finding the general solution of LODEs and a system of two LODEs via two integral transforms, J. Kerbala Univ. 5(1) (2009).
[6] F. Kaya and Y. Yilmaz, Basic properties of Sumudu transformation and its application to some partial differential equations, Sakarya Univ. J. Sci. 23(4) (2019) 509–514.
[7] M.D. Raisinghania, Advanced Differential Equations, S. Chand and Company Ltd, Fourteenth Revised Edition, 2011.
[8] J.L. Schiff, the Laplace Transform: Theory and Applications, Springer-Verlag, New York, Berlin, 1999.
[9] J. Vashi and M.G. Timol, Laplace and Sumudu transforms and their application, Int. J. Innov. Sci. Engin. Technol. 3(8) (2016).
Volume 13, Issue 1
March 2022
Pages 2087-2093
  • Receive Date: 01 November 2021
  • Accept Date: 30 November 2021