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2010•Journal of Qingdao Technological UniversityRequires access

Solving Particular Solutions of Constant Coefficient Non-Homogeneous Nth Order Linear Differential Equations by Linear Transformations

JI Zheb

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Abstract

An undetermined coefficient is a general method of solving the particular solution y* of a non-homogeneous nth order linear differential equation y(n)+a1y(n-1)+…+any=eλx[Pl(x)cosωx+Pn(x)sinωx].This method needs to compute the 1st to nth order derivatives,which is very complex.In the paper these derivatives are expressed by a linear transform into dot products of vectors without being computed any more,which fairly reduces the complexity of calculation.In conclusion,an exemplary application of this method is given.

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What this paper is about

An undetermined coefficient is a general method of solving the particular solution y* of a non-homogeneous nth order linear differential equation y(n)+a1y(n-1)+…+any=eλx[Pl(x)cosωx+Pn(x)sinωx].This method needs to compute the 1st to nth order derivatives,which is very complex.In the paper these derivatives are expressed by a linear transform into dot products of vectors without being computed any more,which fairly reduces the complexity of calculation.In conclusion,an exemplary application of this method is given.

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Available abstract

An undetermined coefficient is a general method of solving the particular solution y* of a non-homogeneous nth order linear differential equation y(n)+a1y(n-1)+…+any=eλx[Pl(x)cosωx+Pn(x)sinωx].This method needs to compute the 1st to nth order derivatives,which is very complex.In the paper these derivatives are expressed by a linear transform into dot products of vectors without being computed any more,which fairly reduces the complexity of calculation.In conclusion,an exemplary application of this method is given.

Key concepts: Homogeneous differential equation, Linear differential equation, Homogeneous, Constant coefficients, Mathematics, Order (exchange), Constant (computer programming), Differential equation

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