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Applied Mathematical Methods by Bhaskar Dasgupta

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35

Higher Order Linear ODE’s

In this chapter, we essentially extend and generalize our work of the previous two chapters for arbitrary order of linear ordinary differential equations. Since a second order linear ODE more or less captures all the major features of linear systems, a direct extension of the concepts and methods is possible, except for some procedural details. As such, in the present chapter, we will avoid repetition of arguments and elaborate more on those aspects where there are differences due to the order of the ODE.

Theory of Linear ODE’s

As with second order ODE’s, the continuity of functions P1 (x), P2(x),⋯, Pn (x) and R (x) guarantees the existence of a solution of the linear ODE

y(n) + P1(x)y(n − 1) + P2(x)y(n − 2) + ⋯ + ...

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