1.1 Definitions and Basic Concepts

• Types of Ordinary Differential Equations
• Systems of ODEs

1.2 Direction Field of First Order ODEs

1.3 The Approaches of Finding Solutions of ODE

• Analytical Approaches
• Numerical Approaches

2. First order ordinary differential equations

2.1 Separable Differential Equations

2.2 Reduction to separable equations.

2.3 Linear Equations

2.4 Exact Differential Equations

2.5 Integrating factor .

2.6 Existence and Uniqueness of Solution

2.7 Application of first order ODEs

• Motion through a resisting medium
• Population growth
• Radioactive decay
• Heating and cooling problems
• Orthogonal trajectories.
• Mixing problems

3. Secocd order ordinary differential equations

3.1 Basic concepts

3.2 Reduction of order

3.3 Homogeneous Equations with Constant Coefficients

• Distinct real roots
• Complex Conjugate Roots
• Repeated Roots . .

3.4 Nonhomogeneous Equations

• Undetermined Coefficients
• Variation of Parameters