Ordinary Differential Equations

What is a DIFFERENTIAL EQUATION?? **Intro to my full ODE course**.
The Key Definitions of Differential Equations: ODE, order, solution, initial condition, IVP.
Separation of Variables // Differential Equations.
Newton's Law of Cooling // Separable ODE Example.
The Geometric Meaning of Differential Equations // Slope Fields, Integral Curves & Isoclines.
The Big Theorem of Differential Equations: Existence & Uniqueness.
Linear Differential Equations & the Method of Integrating Factors.
The Method of Integrating Factors for Linear 1st Order ODEs **full example**.
The Bernoulli Equation // Substitutions in Differential Equations.
Autonomous Equations, Equilibrium Solutions, and Stability.
The Logistic Growth Differential Equation.
The Theory of 2nd Order ODEs // Existence & Uniqueness, Superposition, & Linear Independence.
How to Solve Constant Coefficient Homogeneous Differential Equations.
Constant Coefficient ODEs: Real & Distinct vs Real & Repeated vs Complex Pair.
Higher Order Constant Coefficient Differential Equations: y'''+y'=0 and y''''-3y'''+3y''-y'=0.
Linear Independence of Functions & The Wronskian.
The Theory of Higher Order Differential Equations.
Undamped Mechanical Vibrations & Hooke's Law // Simple Harmonic Motion.
Mechanical Vibrations: Underdamped vs Overdamped vs Critically Damped.
Undetermined Coefficients: Solving non-homogeneous ODEs.
Variation of Parameters || How to solve non-homogeneous ODEs.
How to solve ODEs with infinite series | Intro & Easiest Example: y'=y.
When can you use Series to solve ODEs? Ordinary vs Singular Points.
How to use SERIES to solve DIFFERENTIAL EQUATIONS example: Airy's Equation y''-xy=0.