ABSTRACT
This chapter discusses some general properties of first-order differential equations. The general properties include a classification of solutions and the determination of the arbitrary constant in the general integral. The differential equation is considered to be solved when it is reduced to an integration or quadrature that may be elementary or not. The chapter presents methods of solution for the separable equation, the linear unforced equation, the linear forced equation, the Bernoulli equation, and the Riccati equation. A first-order differential equation specifies one slope at each point of the plane if it is explicit; that is, has only one root for the slope. The curve with this slope is an integral curve, or particular integral of the differential equation. Since there is an integral curve through every regular point, they form a family of curves involving an arbitrary constant; that is, the general integral of the differential equation.
