1. Introduction to Differential Equations

This chapter lays the foundation for you to learn ordinary differential equations by touching on basic concepts in differential equations particularly ordinary differential equations, and some analytical methods for solving ordinary differential equations.

After completing this chapter, you should be able to

• Identify the type, order, degree, linearity and homogeneity of differential equations;

• Understand the definition of initial value problems;

• Find analytical solutions to separable first-order ordinary differential equations;

• Find analytical solutions to linear ordinary differential equations with constant coefficients.

• 1.1. Definitions, Classification and Terminology
• 1.2. Ordinary Differential Equations
• 1.3. Analytical Methods for ODEs
• 1.4. Applications of ODEs
• 1.5. Chapter 1 Exercises