Notes on Elementary Differential Equations (Kasali)

Course Scope and Core Concepts

  • Elementary Differential Equations (EDE) course at First Technical University, Ibadan, offers a structured introduction to ODEs and basic difference equations, focusing on techniques for first-order and some second-order problems.
  • Core focus areas include: definitions, order and degree, formation of differential equations, and classical solution techniques for first- and second-order problems.
  • Notation and terms to know:
    • ODE: differential equation involving ordinary derivatives (dy/dx, d^2y/dx^2, etc.).
    • PDE: differential equation involving partial derivatives (∂z/∂x, ∂^2z/∂x∂y, etc.).
  • This course centers on Ordinary Differential Equations (ODE) only, not PDEs.

Basic Definitions: Differential Equations, ODE vs PDE

  • A differential equation involves the dependent variable and its derivatives with respect to an independent variable(s).
  • Examples:
    • racdydx−4y=6x2rac{dy}{dx} - 4y = 6x^2
    • rac{ rac{ ext{d}^2 z}{ ext{d} x^2} }{ ext{d}x^2 } - rac{ rac{ ext{d}^2 z}{ ext{d} y^2} }{ ext{d}y^2 } = 1, ext{ with } z=z(x,y)
  • Classification:
    • ODE: differential equation involving ordinary derivatives only, e.g., $$ rac{dy}{dx}, rac{d^2y}{dx^2}, \