Differential Equation:
A differential equation is a mathematical equation that relates some function with its derivatives. It expresses how a function changes over time or space. Differential equations are used to model various phenomena in physics, engineering, economics, and other fields.

Ordinary Differential Equation (ODE):
- An ordinary differential equation involves a single independent variable and its derivatives.
- ODEs are used to model dynamic systems where the unknown function depends on only one variable.
- Examples of ODEs include Newton's law of cooling and population growth models.

Partial Differential Equation (PDE):
- A partial differential equation involves multiple independent variables and their partial derivatives.
- PDEs are used to describe systems that depend on multiple variables, such as heat conduction or fluid dynamics.
- They are essential in physics and engineering for modeling complex phenomena.
In summary, a differential equation is a mathematical equation that relates a function and its derivatives. Ordinary differential equations deal with one independent variable, while partial differential equations involve multiple independent variables. These equations play a crucial role in modeling various real-world phenomena and are widely used in different fields of science and engineering.