International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 08 Issue: 02 | Feb 2021 www.irjet.net p-ISSN: 2395-0072 © 2021, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 544 Applications of Differential Transform Method Dr. Sarita Devi 1 , Dr. Manjeet Jakhar 2 1 Assistant professor, Department of Applied Sciences and Humanities, Pillai HOC college of Engineering and Technology, Rasayani, Navi Mumbai (Maharashtra), India. 2 Assistant professor, Department of Mathematics, NIILM University, Kaithal, Haryana, India. 1 sarita2009devi@gmail.com, 2 dr.manjeet.jakhar@gmail.com promising to a broad class of linear and non-linear problems. The result of differential transform method is in good agreement with those obtained by using already existing ones. The differential transform method appeared to be effective, reliable, easy and flexible for finding the solutions for such type of initial value problems. DTM is an analytical & numerical method for solving a wide variety of numerical differential equations and usually gets the solution in series form. Keywords: Initial value problems, Linear, Non-linear, Differential transform, Numerical method. 1. Introduction Many problems of different fields like engineering, physics and geology are described by ordinary or partial differential equations with appropriate value problems. The differential transform method is very effective and powerful tool for solving various kinds of differential equations. Zhou introduced the basic idea of DTM in 1980, to solve linear and non- linear initial value problem that applies in electrical circuits. DTM is an iterative procedure for obtaining analytical Taylor Series solution of differential equations. The Taylor series method computationally takes long time for large orders. The main advantage of this method is that this can be applied directly to differential equations without recurring linearization, discretization. 2. Differential transform method (DTM): Differential transform of the function y(x), is defined as follows: ……………………………………………………………………………(1) and inverse differential transform of Y(k) is defined by: ………………………………………………...........………………...............…(2) Based on the above definitions, the fundamental operations of differential transform method as shown below: 3. One dimensional differential transformation: 3.1. If y(x) = w(x) ± z(x), then, Y (k) = W (k) ± Z (k) 3.2. If y(x) = c w(x), then, Y (k) = c W (k), where “c” is constant. 3.3. If y(x) = (dw(x))/dx, then, Y (k) = (k+1) W (k). 3.4. If y(x) = (d^m w(x))/ (dx^m), then, Y (k) = (k+1) (k+2) -------- (k+m) W (k+m). ---------------------------------------------------------------------------***---------------------------------------------------------------------------- Abstract: In this paper, the initial value problem is solved by differential transform method. The proposed method is