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# Solving the Systems of Differential Equations by a Power Series Method

 A. Pourhabib Yekta1, A. Khoshkenar2 Department of Mathematics, Sowmesara Branch, Islamic Azad University, Sowmesara, Iran. Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran Related article at Pubmed, Scholar Google

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## Abstract

In this article power series method, as well-known method for solving ordinary differential equations, has been employed to solve linear systems of first order differential equations. Theoretical considerations and convergence of the method for these systems are discussed. Some examples are presented to show the ability of the method for such systems.

### Keywords

Power Series Method, Linear Systems of Ordinary Differential Equations.

### INTRODUCTION

A linear system of first order differential equations can be considered, as:

### CONCLUSION

Power series method has been known as a powerful device for solving second order linear differential equations. Here we used this method for solving linear system of first order differential equations. The convergency of solutions has been shown. We present three examples and as it shown this method has the ability of solving such systems.

### ACKNOWLEDGEMENTS

We are extremely thankful and pay our gratitude to Islamic Azad University of Sowmesara for financially support on completion of this project in its presently.

### References

[1] G. F. Simons, Differential equation with application and historical notes, TATA Mc Graw-Hill Publication Company LTD, 1979.

[2] J. Biazar, M. Ilie, A. Khoshkenar, A new approach to the solution of the prey and predator problem and comparison of the results with the Adomian method, Applied Mathematics and Computation, 171 (2005) 486-491.

[3] A. Khoshkenar, M. Ilie, M. Saeeidi. The power series with functional coefficiens and its application for solving the partial differential equations with initial conditions, Journal of applied mathematics, Vol. 6 No. 20