Abstract
Separable, linear, and autonomous equations; equilibrium solutions, stability and bifurcation. Other special types of equations, for example, Bernoulli, exact, and homogeneous equations, are covered in the Exercises with generous guidance. Many applications are discussed from science, engineering, economics, and biology.
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Notes
- 1.
We are overburdening the notation by using the same symbol \(x\) to denote both a variable and a function. It would be more precise to write “\(x=\varphi (t)\) is a solution,” but we choose to stick to the common use, and abuse, of a single letter.
- 2.
A quantity \(Q\) is jointly proportional to quantities \(A\) and \(B\) if \(Q=kAB\) for some constant k.
- 3.
We use subscripts to denote partial derivatives, and so \(f_{x}=\partial f / \partial x.\)
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© 2015 Springer International Publishers, Switzerland
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Logan, J. (2015). First-Order Differential Equations. In: A First Course in Differential Equations. Undergraduate Texts in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-17852-3_1
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DOI: https://doi.org/10.1007/978-3-319-17852-3_1
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-17851-6
Online ISBN: 978-3-319-17852-3
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