Ordinary Differential Equations

Educational level: this is a tertiary (university) resource.

Subject classification: this is a mathematics resource.

Completion status: this resource is just getting off the ground. Please feel welcome to help!

• See also Differential equations/Ordinary Differential Equations

Contents

• Basic Concepts
  • What is a differential equation?
  • Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs)
  • Order of an ODE
  • Linear and Non-linear ODEs
• ODEs as Models
• Verifying Solutions to ODEs
• Initial Value Problems (IVP)
• First Order ODEs
  • Direction Fields
  • Separable Equations
  • Method of Integrating Factors
  • Exact Equations
  • Euler's Method
  • Systems of ODEs
  • The Existence and Uniqueness Theorem
• Second Order ODEs
  • Solving Constant Coefficient Second Order Homegenous ODEs ${\displaystyle ay''+by'+cy=0}$
    • Case with Complex Roots
    • Case with Repeated Roots