First-Order ODEs

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

Chapter Chapter 2 in Ordinary Differential Equations and Mechanical Systems, 2014, pp 13-50 from Springer

Abstract: Abstract Modelling of various problems in engineering, physics, chemistry, biology and economics allows formulating of differential equations, where a being searched function is expressed via its time changes (velocities). One of the simplest example is that given by a first-order ODE of the form 2.1 d y d t = F ( y ) , $$\displaystyle{ \frac{dy} {dt} = F(y), }$$ where F(t) is a known function, and we are looking for y(t). Here by t we denote time. In general, any given differential equation has infinitely many solutions. In order to choose from infinite solutions those corresponding to a studied real process, one should attach initial conditions of the form y ( t 0 ) = y 0 $$y(t_{0}) = y_{0}$$ .

Keywords: First-order ODEs; Infinite Solutions; Exact Differential Equation; Full Differential; Bernoulli Method (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-07659-1_2

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