Abstract
Chapter 2 deals with scalar first-order differential equations. The existence and uniqueness of solutions of initial value problems is studied on the basis of the well-known theorems of Peano and Picard-Lindelöf. The analytical standard techniques for the determination of the exact solution are given. Moreover, the solution of high-degree first-order differential equations (Clairaut and Lagrange equation) that are often encountered in the applications is discussed. The chapter ends with the discussion about family of curves and orthogonal trajectories.
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Reference
Hartman, P.: Ordinary Differential Equations. Birkhäuser, Boston/Basel/Stuttgart (1982)
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© 2014 Springer India
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Hermann, M., Saravi, M. (2014). First-Order Differential Equations . In: A First Course in Ordinary Differential Equations. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1835-7_2
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DOI: https://doi.org/10.1007/978-81-322-1835-7_2
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Publisher Name: Springer, New Delhi
Print ISBN: 978-81-322-1834-0
Online ISBN: 978-81-322-1835-7
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