This section is devoted to ordinary differential equations of the second order. In the beginning, we consider different types of such equations and examples with detailed solutions. The following topics describe applications of second order equations in geometry and physics.

- 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 Equation
- Chebyshev 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