Differential Equations

A differential equation is a mathematical equation that relates some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two.

•  What is a differential equation
  
•  Separable Differential Equations
  
•  Separable differential equations 2
  
•  Exact Equations Intuition 1 (proofy)
  
•  Exact Equations Intuition 2 (proofy)
  
•  Exact Equations Example 1
  
•  Exact Equations Example 2
  
•  Exact Equations Example 3
  
•  Integrating factors 1
  
•  Integrating factors 2
  
•  First order homegenous equations
  
•  First order homogenous equations 2
  
•  2nd Order Linear Homogeneous Differential Equations 1
  
•  2nd Order Linear Homogeneous Differential Equations 2
  
•  2nd Order Linear Homogeneous Differential Equations 3
  
•  2nd Order Linear Homogeneous Differential Equations 4
  
•  Complex roots of the characteristic equations 1
  
•  Complex roots of the characteristic equations 2
  
•  Complex roots of the characteristic equations 3
  
•  Repeated roots of the characteristic equation
  
•  Repeated roots of the characterisitic equations part 2
  
•  Undetermined Coefficients 1
  
•  Undetermined Coefficients 2
  
•  Undetermined Coefficients 3
  
•  Undetermined Coefficients 4
  
•  Laplace Transform 1
  
•  Logistic Differential Equation
  
•  Euler’s Method – Another Example 2
  
•  Euler’s Method – Another Example 1
  
•  Solving a Separable Differential Equation, Another Example 5, Initial Condition
  
•  Solving a Separable Differential Equation, Another Example 4, Initial Condition
  
•  Basic Differential Equation with an Initial Condition
  
•  Solving a Separable Differential Equation, Another Example 3
  
•  Solving a Separable Differential Equation, Another Example 2
  
•  Solving a Separable Differential Equation, Another Example 1
  
•  Differential Equations – Basic Idea of What It Means to be a Solution
  
•  First Order Linear Differential Equations / Integrating Factors – Ex 2
  
•  Change of Variables / Homogeneous Differential Equation – Example 4
  
•  Change of Variables / Homogeneous Differential Equation – Example 3
  
•  Change of Variables / Homogeneous Differential Equation – Example 2
  
•  Change of Variables / Homogeneous Differential Equation – Example 1
  
•  The Inverse Laplace Transform – Example and Important Theorem
  
•  Table of Laplace Transforms
  
•  Laplace Transform 2
  
•  Laplace Transform 3 (L{sin(at)})
  
•  Laplace Transform 4
  
•  Laplace Transform 5
  
•  Laplace Transform 6
  
•  Laplace Transform to solve an equation
  
•  Laplace Transform solves an equation 2
  
•  More Laplace Transform tools
  
•  Using the Laplace Transform to solve a nonhomogenous eq
  
•  Laplace Transform of : L{t}
  
•  Laplace Transform of t^n: L{t^n}
  
•  Laplace Transform of the Unit Step Function
  
•  Inverse Laplace Examples
  
•  Laplace/Step Function Differential Equation
  
•  Dirac Delta Function
  
•  Laplace Transform of the Dirac Delta Function
  
•  Introduction to the Convolution
  
•  The Convolution and the Laplace Transform
  
•  Using the Convolution Theorem to Solve an Initial Value Prob
  
•  Laplace Transform is a Linear Operator – Proof
  
•  The Laplace Transform – More Derivatives
  
•  The Laplace Transform, Basic Properties – Definitions and Derivatives
  
•  The Laplace Transform – The Basic Idea of How We Use It
  
•  The Logistic Equation and Models for Population – Example 1, part 2
  
•  The Logistic Equation and Models for Population – Example 1, part 1
  
•  The Logistic Equation and the Analytic Solution
  
•  Power Series Solutions of Differential Equations
  
•  Exact Differential Equations
  
•  First Order Linear Differential Equations
  
•  Reduction of Order, Basic Example