# Differential Equations

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## First Order Differential Equations

- Separable Equations
- Homogeneous Equations
- Linear Differential Equations of First Order
- Exact Differential Equations
- Using an Integrating Factor
- Bernoulli Equation
- Riccati Equation
- Implicit Differential Equations
- Singular Solutions of Differential Equations
- Lagrange and Clairaut Equations
- Differential Equations of Plane Curves
- Orthogonal Trajectories
- Radioactive Decay
- Barometric Formula
- Rocket Motion
- Newton’s Law of Cooling
- Fluid Flow from a Vessel
- Population Growth
- Learning Curve
- Advertising Awareness

## Second Order Differential Equations

- Reduction of Order
- Second Order Linear Homogeneous Differential Equations with Constant Coefficients
- Second Order Linear Nonhomogeneous Differential Equations with Constant Coefficients
- Second Order Linear Homogeneous Differential Equations with Variable Coefficients
- Second Order Linear Nonhomogeneous Differential Equations with Variable Coefficients
- Second Order Euler Equation
- Bessel Differential Equation
- Chebyshev Differential Equation
- Curvature of Plane Curves
- Equation of Catenary
- Newton’s Second Law of Motion
- Newton’s Law of Universal Gravitation
- Mechanical Oscillations
- Nonlinear Pendulum
- Oscillations in Electrical Circuits

## Higher Order Differential Equations

- Cases of Reduction of Order
- Equations Solvable in Quadratures
- Differential Operators
- Higher Order Linear Homogeneous Differential Equations with Constant Coefficients
- Higher Order Linear Nonhomogeneous Differential Equations with Constant Coefficients
- Higher Order Linear Homogeneous Differential Equations with Variable Coefficients
- Higher Order Linear Nonhomogeneous Differential Equations with Variable Coefficients
- Higher Order Euler Equation
- Beam Deflection

## Systems of Differential Equations

- Linear Homogeneous Systems of Differential Equations with Constant Coefficients
- Method of Eigenvalues and Eigenvectors
- Construction of the General Solution of a System of Equations Using the Method of Undetermined Coefficients
- Construction of the General Solution of a System of Equations Using the Jordan Form
- Method of Matrix Exponential
- Linear Nonhomogeneous Systems of Differential Equations with Constant Coefficients
- Linear Systems of Differential Equations with Variable Coefficients
- Basic Concepts of Stability Theory
- Equilibrium Points of Linear Autonomous Systems
- Stability in the First Approximation
- Method of Lyapunov Functions
- Routh-Hurwitz Criterion
- First Integrals
- Mass-Spring System
- Double Pendulum
- Home Heating