Higher-Order ODEs Polynomial Form

Jan Awrejcewicz
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Jan Awrejcewicz: Łódź University of Technology, Department of Automation, Biomechanics and Mechatronics

Chapter Chapter 5 in Ordinary Differential Equations and Mechanical Systems, 2014, pp 221-243 from Springer

Abstract: Abstract If a function f ( t , x , ẋ , … , x ( n ) ) $$f(t,x,\dot{x},\ldots,x^{(n)})$$ is defined and is continuous in a subset of ℝ n + 2 ( n ≥ 1 ) $$\mathbb{R}^{n+2}(n \geq 1)$$ , then the equation 5.1 f ( t , x , ẋ , … , x ( n ) ) = 0 $$\displaystyle{ f(t,x,\dot{x},\ldots,x^{(n)}) = 0 }$$ is said to be ordinary differential equation of nth-order.

Keywords: Euler-Cauchy Differential Equation; Independent Real-valued Solutions; Complex-valued Roots; Subkernel; Undetermined Coefficients (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-07659-1_5

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DOI: 10.1007/978-3-319-07659-1_5

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