JAMP  Vol.8 No.7 , July 2020
Frobenius Method for Solving Second-Order Ordinary Differential Equations
Abstract: As we know that the power series method is a very effective method for solving the Ordinary differential equations (ODEs) which have variable coefficient, so in this paper we have studied how to solve second-order ordinary differential equation with variable coefficient at a singular point t = 0 and determined the form of second linearly independent solution. Based on the roots of initial equation there are real and complex cases. When the roots of initial equation are real then there are three kinds of second linearly independent solutions. If the roots of the initial equation are distinct complex numbers, then the solution is complex-valued.
Cite this paper: Torabi, A. and Rohani, M. (2020) Frobenius Method for Solving Second-Order Ordinary Differential Equations. Journal of Applied Mathematics and Physics, 8, 1269-1277. doi: 10.4236/jamp.2020.87097.

[1]   Adkins, W. and Davidson, M.G. (2010) Ordinary Differential Equation. Springer, New York.

[2]   Kreyszig, E. (2006) Advance Engineering Mathematics. 9th Edition, Willy Ltd., India.

[3]   Haarsa, P. and Pothat, S. (2014) The Frobenius Method on a Second Order Homogeneous Linear ODEs. Advance Studies in Theoretical Physics, 8, 1145-1148.

[4]   Syofra, A.H., Permatasari, R. and Nazara, A. (2016) The Frobenius Method for Solving Ordinary Differential Equation with Coefficient Variable. IJSR, 5, 2233-2235.

[5]   Hartman, P. (2002) Ordinary Deferential Equation. 2nd Edition, SIAM, Philadelphia.

[6]   Birkhoff, G. and Rota, G.-C. (1989) Ordinary Differential Equation. 4th Edition, Wily, New York.