Differential Equations

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