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PENGGUNAAN METODE FROBENIUS UNTUK MENYELESAIKAN PERSAMAAN DIFERENSIAL BESSEL DAN APLIKASINYA PADA GETARAN RANTAI YANG BERGANTUNG

MARIYA ULFA, SITI (2012) PENGGUNAAN METODE FROBENIUS UNTUK MENYELESAIKAN PERSAMAAN DIFERENSIAL BESSEL DAN APLIKASINYA PADA GETARAN RANTAI YANG BERGANTUNG. Other thesis, University of Muhammadiyah Malang.

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Abstract

solution of differential equations can be used many ways depending on the classification of differential equations. Frobenius method is the development of the power series method is one way to solve differential equations with variable coefficients. Solution of differential equations using the Frobenius method can only be done if the equation has a singular point. Differential equation of Bessel of the form x^2 y^''+xy^'+(x^2-v^2 )y=0 is an equation that has one singular point at x=0 and can be solved using the method of Frobenius. Completion using the Frobenius method can be done by letting solution equation into the form of the series and transform the initial equation into the form of the series so obtained indical equation. Base solution can be sought by considering the roots of the equation is based indical theorems are then derived the general solution of differential equations in the form of the series y(x)=C_1 y_1 (x)+C_2 y_2 (x) with C_1 and C_2 is an arbitrary constant. The application of differential equations are found in everyday life and in various fields. One of them in the field of physics, namely the problem of vibration-dependent chain. At the time of the chain hanging vertically and t=0 so that an angle α, if the chain is released then there is a change of style. Changes in the style which then form the Bessel differential equation (d^2 y)/〖ds〗^2 +1/s dy/ds+y=0 with parameter v = 0. Looking solution these equations can use Frobenius method to the roots of the indical equation r=0.

Item Type: Thesis (Other)
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Teacher Training and Education > Department of Mathematics Education (84202)
Depositing User: Gusti Vani Putri Cahya
Date Deposited: 03 Feb 2015 03:38
Last Modified: 03 Feb 2015 03:38
URI : http://eprints.umm.ac.id/id/eprint/15557

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