Albert Science International Organization

Abstract: In this paper, the solutions of higher order differential equations with constant co-efficient are obtained by applying Dinesh Verma Transform (DVT). The boundary value problems described by higher order linear ordinary differential equations in science and engineering are analyzed by Dinesh Verma Transform (DVT). It is revealed that the higher order linear ordinary differential equations in science and engineering are easily analyzed by Dinesh Verma Transform (DVT).

Index Terms: Dinesh Verma transform (DVT), Higher Order Linear Ordinary Differential equations.

 [1] H.K. Dass, Introduction to Engineering Mathematics.

 [2] Erwin Kreyszig, Advanced Engineering Mathematics, Wiley, 1998.

  [3] Dinesh Verma, Putting Forward a Novel Integral Transform: Dinesh Verma Transform (DVT) and its Applications, International Journal of Scientific Research in Mathematical   and Statistical Sciences, Volume -7, Issue-2, April-2020.

  [4] Rohit Gupta, Rahul Gupta, Dinesh Verma, Eigen Energy Values and Eigen Functions of a Particle in an Infinite Square Well Potential by Laplace Transforms, International       Journal of Innovative Technology and Exploring Engineering, Volume-8 Issue-3, January 2019.

   [5] Rahul gupta and Rohit gupta, “Laplace Transform method for obtaining the temperature distribution and the heat flow along a uniform conducting rod connected between two          thermal reservoirs maintained at different temperatures”, Pramana Research Journal, Volume 8, Issue 9, 2018, pp. 47-54.

[6] Tarig M. Elzaki, Salih M. Elzaki and Elsayed Elnour, On the new integral transform Elzaki transform fundamental properties investigations and applications, global journal of mathematical sciences: Theory and Practical, volume 4, number 1(2012).

[7] Sadikali Latif Shaikh, Introducing a new integral transform: Sadik Transform, American International Journal of Research in Science, Technology, Engineering & Mathematics, 22(1), March-May 2018, pp.100-102.

[8] Abdelilah Kamal, H. Sedeeg, The New Integral Transform ''Kamal Transform'', Advances in Theoretical and Applied Mathematics ISSN 0973-4554 Volume 11, Number 4 (2016), pp. 451-458.

[9] Mohand, D., Aboodh, K.S. and Abdelbagy, A., On the solution of ordinary differential equation with variable coefficients using Aboodh transform, Advances in Theoretical and Applied Mathematics, 11(4), 383-389, 2016.

[10] Khalid Suliman Aboodh, The New Integral Transform ''Aboodh Transform'', Global Journal of Pure and Applied Mathematics, ISSN 0973-1768 Volume 9, Number 1 (2013), pp. 35-43.

[11] Mohand M. Abdelrahim Mahgoub, The New Integral Transform ''Mohand Transform”, Advances in Theoretical and Applied Mathematics, ISSN 0973-4554, Volume 12, Number 2 (2017), pp. 113-120.

[12] Belgacem, F.B.M. and Karaballi, A.A., Sumudu transform fundamental properties investigations and applications, Journal of Applied Mathematics and Stochastic Analysis, 1-23, 2006.

[13] Maitama, S. and Zhao, W., New integral transform: Shehu transform a generalization of Sumudu and Laplace transform for solving differential equations, International Journal of Analysis and Applications, 17(2), 167-190, 2019.

[14] Mahgoub, M.A.M., The new integral transform “Mahgoub Transform”, Advances in Theoretical and Applied Mathematics, 11(4), 391-398, 2016.

[15] Mr. Kharde Uttam Dattu, New Integral Transform: Fundamental Properties, Investigations and Applications, IAETSD Journal for Advanced Research in Applied Sciences, volume 5, issue 4, April/2018.

[16] Rahul Gupta, Rohit Gupta, Dinesh Verma, Application of Convolution Method to the Impulsive Response of A Lightly Damped Harmonic Oscillator, International Journal of Scientific Research in Physics and Applied Sciences ,Vol.7, Issue.3, pp.173-175, June (2019).

[17] Rahul Gupta,Rohit Gupta and Dinesh Verma, Application of Novel Integral Transform: Gupta Transform to Mechanical and Electrical Oscillators,  ASIO Journal of Chemistry, Physics, Mathematics & Applied Sciences (ASIO-JCPMAS), Volume -4, Issue-1, 2020.

[18] Dinesh Verma, Applications of Laplace Transformation for solving Various Differential Equations with Variable Coefficients, International Journal for Innovative Research in Science & Technology, Volume 4, Issue 11, April 2018.

[19] Dinesh Verma, Elzaki Transform Approach to Differential Equatons with Leguerre Polynomial, International Research Journal of Modernization in Engineering Technology and Science (IRJMETS), Volume-2, Issue-3, March  2020.

[20] Mohand M. Abdelrahim Mahgoub, Khalid Suliman Aboodh, Abdelbagy A. Alshikh, On The Solution of Ordinary Differential Equation with Variable Coefficients using Aboodh Transform,  Advances in Theoretical and Applied Mathematics ISSN 0973-4554 Volume 11, Number 4 (2016), pp. 383-389.

[21] Murray R. Spiegel, Theory and Problems of Laplace Transforms, Schaum's outline series, McGraw - Hill.

[22] Sunil Shrivastava, Introduction of Laplace Transform and Elzaki Transform with Application (Electrical Circuits),International Research Journal of Engineering and Technology (IRJET) ,volume 05, Issue 02 , Feb. 2018.

[23] P. Senthil Kumar, S. Vasuki, Applications of Aboodh Transform to Mechanics, Electrical Circuit Problems, International Journal for Research in Engineering Application & Management (IJREAM) ISSN : 2454-9150 Vol-04, Issue-06, Sep 2018.

[24] P. Senthil Kumar, A. Viswanathan, Applications of Mahgoub Transform to Mechanics, Electrical Circuit Problems, International Journal of Science and Research (IJSR), Volume 7 Issue 7, July 2018.

[25] Dinesh Verma, Aftab Alam, Analysis of Simultaneous    Differential Equations by Elzaki Transform Approach, Journal of Science, Technology and Development, Volume IX Issue I January 2020.

[26] Dinesh Verma, Elzaki Transform of some significant Infinite Power Series, International Journal of Advance Research and Innovative Ideas  in Education (IJARIIE), Volume-6, Issue-1, February  2020.

 [27] Rohit Gupta, Amit Pal Singh, Dinesh Verma, Flow of Heat Through A Plane Wall, And Through A Finite Fin Insulated At The Tip, International Journal Of Scientific & Technology Research, Volume 8, Issue 10, October 2019.

[28] Rohit Gupta, Neeraj Pandita and Dinesh Verma ,Conduction of Heat Through the Thin and Straight Triangular Fin, ASIO Journal of Engineering & Technological Perspective Research (ASIO-JETPR) Volume -5, Issue-1, 2020.

 [29] Dinesh Verma, A Laplace Transformation approach to Simultaneous Linear Differential Equations, New York Science Journal” Volume-12, Issue-7, July 2019.

[30] Dinesh Verma, A Useful technique for solving the differential equation with boundary values, Academia Arena” Volume-11, Issue-2, 2019.

[31] Dinesh Verma, Relation between Beta and Gamma function by using Laplace Transformation, Researcher, Volume-10, Issue-7, 2018.

[32] Dinesh Verma , An overview of some special functions, International Journal of Innovative Research in Technology (IJIRT), Volume-5, Issue-1, June 2018.

[33] Dinesh Verma, Applications of Convolution Theorem, International Journal of Trend in Scientific Research and Development (IJTSRD), Volume-2, Issue-4, May-June 2018.

[34]  Dinesh Verma, Solving Fourier Integral Problem by Using Laplace Transformation, International Journal of Innovative Research in Technology (IJIRT), Volume-4, Issue-11, April 2018.

[35] Dinesh Verma, Applications of Laplace Transformation for solving Various Differential equations with variable co-efficient, International Journal for Innovative Research in Science and Technology (IJIRST),Volume-4, Issue-11, April 2018.

[36]  Dinesh Verma and Amit Pal Singh, Applications of Inverse Laplace Transformations, Compliance Engineering Journal, Volume-10, Issue-12, December 2019, ISSN 0898-3577; PP: 305-308.

[37] Rahul gupta, Rohit gupta and Dinesh Verma, Propounding a New Integral Transform: Gupta Transform with Applications in Science and Engineering, International Journal of scientific research in multidisciplinary studies (IJSRMS), Volume-6, Issue-3, March 2020.

[38] Dinesh Verma, Signification of Hyperbolic Functions and Relations, International Journal of Scientific Research & Development (IJSRD), Volume-07, Issue-5, May 2019.

[39] Dinesh Verma, Yubraj Singh and Rohit Gupta, Response of Electrical Networks with Delta Potential via Mohand Transform, International Research Journal of Innovations in Engineering and Technology (IRJIET) ,Volume-4, Issue-2, February  2020.

[40] Dinesh Verma and Rahul Gupta “Delta Potential Response of Electric Network Circuit, Iconic Research and Engineering Journal (IRE)” Volume-3, Issue-8, February 2020.