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First-Order ODEs

In: Ordinary Differential Equations and Mechanical Systems

Author

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  • Jan Awrejcewicz

    (Łódź University of Technology, Department of Automation, Biomechanics and Mechatronics)

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 $$y(t_{0}) = y_{0}$$ .

Suggested Citation

  • Jan Awrejcewicz, 2014. "First-Order ODEs," Springer Books, in: Ordinary Differential Equations and Mechanical Systems, edition 127, chapter 0, pages 13-50, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-07659-1_2
    DOI: 10.1007/978-3-319-07659-1_2
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