Differential equation

Definition

A differential equation is an equation that relates a function with its derivatives. It describes how a quantity changes over time or space.

5 Must Know Facts For Your Next Test

1. Differential equations can be classified as ordinary (ODE) or partial (PDE).
2. The order of a differential equation is determined by the highest derivative present.
3. Solutions to differential equations can be general (including constants) or particular (specific solutions).
4. Linear differential equations have solutions that can be superimposed, while nonlinear ones do not.
5. Initial conditions are often required to find a unique solution to a differential equation.

Review Questions

• What distinguishes an ordinary differential equation from a partial differential equation?
• How do you determine the order of a given differential equation?
• Why are initial conditions important in solving differential equations?

Related terms

Ordinary Differential Equation (ODE): A type of differential equation involving functions of only one variable and their derivatives.

Partial Differential Equation (PDE): A type of differential equation involving multiple variables and their partial derivatives.

Initial Condition: \text{Values specified for the function and its derivatives at a particular point, used to find unique solutions.}