First-Order Differential Equations

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.