First-Order Differential Equations

Martin Hermann and Masoud Saravi
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Martin Hermann: Friedrich Schiller University, Institute of Applied Mathematics
Masoud Saravi: Islamic Azad University Nour Branch, Department of Mathematics

Chapter Chapter 2 in A First Course in Ordinary Differential Equations, 2014, pp 11-44 from Springer

Abstract: 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.

Keywords: Orthogonal Trajectories; Lagrange Equations; Standard Analytical Techniques; Clairaut Equation; First-order Linear ODEs (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-81-322-1835-7_2

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