International Research Journal of Engineering and Technology (IRJET)
e-ISSN: 2395-0056
Volume: 10 Issue: 04 | Apr 2023
p-ISSN: 2395-0072
www.irjet.net
Solution of Ordinary Differential Equation with Initial Condition Using New Elzaki Transform Sunil Shrivastava1, Dr. Kalpana Saxena2 1Assistant professor, Department of Mathematics, Rabindra nath Tagore University, Bhopal(M.P.) 2Proffessor, Department of Mathematics, Govt. Motilal Vigyan Mahavidyalya, Bhopal(M.P.)
---------------------------------------------------------------------***-------------------------------------------------------------------Elzaki transform define for function of exponential Abstract- In this paper the solution of Ordinary order, function
Differential Equation with initial condition by using the new Elzaki transform is introduced. The new Elzaki transform is modified version of Laplace and Sumudu transform, and it also expand the nth order derivatives by mathematical induction method. Also in this paper we have explained the properties of Elzaki transform, with inversion form of the transform. With this application we can generate simple formula for solving First order first degree, and Second order first degree ordinary differential equations, with constant coefficients. Keywords: equations.
Elzaki
transform
Ordinary
define with a set A below,
| |
|
{
|
} Hear constant M must be real finite number and may be finite or infinite. Elzaki transform denoted by operator E,
differential
{
}
∫
AMS Subject Classification: 44AXX, 34A30, 34A12.
1. INTRODUCTION
2. ELZAKI TRANSFORM OF SOME FUNCTIONS
Ordinary differential equations are used in many areas of engineering and basic science like application Beams, Electrical circuits, Dynamics, etc the Laplace transform are some of the well known ordinary differential equations used in these fields. Many type of Ordinary differential equations also can be solved with aid of integral transforms such as Laplace transform, Fourier transform, Sumudu transform[1,5]. In this paper, we have studied to obtain a formula for a special solution of in the most general case nth order Ordinary Differential Equations with constant coefficient. Also found the solution of first order first degree & second order first degree linear differential equation with constant coefficient [3,4].
{
}
{
}
1
The Elzaki transform method used in several areas of mathematics is an integral transform. We can solve linear differential equation with use Elzaki transform operator moreover partial differential equations, integral equations & integro differential equations. This method can not be suitable for solution of non-linear differential equations. However non-linear differential equation can be solved by using Elzaki transform aid with differential transform method.
© 2023, IRJET
|
Impact Factor value: 8.226
|
ISO 9001:2008 Certified Journal
|
Page 179