This document discusses differential equations and their solutions. It defines differential equations as equations involving derivatives. It notes that solutions can be general, containing an arbitrary constant, or particular, containing an initial value. Examples are given of separating variables and integrating to find the general solution to first order differential equations.

1. CHAPTER 2 Differential Equation

2. Introduction Consider x as an independent variable and y as dependent variable. An equation that involves at least one derivative of y with respect to x, e.g. Is known as a differential equation or common differential equation .

3. b) c) d) a) Example of Differential Equation

8. Example First we must separate the variables: Multiply throughout by dx Divide throughout by y Divide throughout by x

9. This gives us: We now integrate ,

10. Example First we must separate the variables: Multiply throughout by dx Divide throughout by Divide throughout by

15. The General Solution :

18. Exercise : Solve the initial value problem. Express the solution implicitly. a. b.