Differential equation

A differential equation is a mathematical equation that relates some function with its derivatives.

Applications

In applications:

• Functions usually represent physical quantities
• Derivatives represent their rates of change
• The equation defines a relationship between the two

Disciplines

Such relations are common; differential equations play a prominent role in many disciplines, including:

• Engineering
• Physics
• Economics
• Biology

Pure mathematics

In pure mathematics, differential equations are studied from several different perspectives, mostly concerned with their solutions -- the set of functions that satisfy the equation.

Only the simplest differential equations are solvable by explicit formulas; however, some properties of solutions of a given differential equation may be determined without finding their exact form.

Approximation using computers

If a self-contained formula for the solution is not available, the solution may be numerically approximated using computers.

The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations

Numerical analysis can yield solutions with a given degree of accuracy.

See also

• Complex differential equation
• Control theory
• Derivative
• Engineering
• Equations of motion
• Exact differential equation
• Finite difference method
• Function (mathematics)
• Initial condition
• Integral equation
• Mathematical model
• Mathematics
• Numerical analysis
• Picard–Lindelöf theorem on existence and uniqueness of solutions

Recurrence relation, also known as 'Difference Equation'* Physics

• Strange attractor

External links

• Differential equation @ Wikipedia