Introduction to Differential Equations

Flashcards focusing on key terms and definitions related to differential equations.

Differential Equation

An equation containing the derivatives of a function.

Ordinary Differential Equation (ODE)

A differential equation that contains derivatives of a function with respect to a single independent variable.

Partial Differential Equation (PDE)

A differential equation containing derivatives of a function with respect to two or more independent variables.

Order of a Differential Equation

The order of a differential equation is the order of the highest derivative present in the equation.

Degree of a Differential Equation

The highest power of the dependent variable of a differential equation.

Linear Differential Equation

A differential equation where the function and its derivatives appear to the power of one.

Nonlinear Differential Equation

A differential equation which cannot be classified as linear.

General Solution

A solution that contains arbitrary constants and represents a family of functions.

Particular Solution

Solutions established by assigning specific values to arbitrary constants of the general solution.

Implicit Solution

A solution of a differential equation that is given in the form F(x, y) = 0.

Initial Value Problem

A problem of finding a solution to a differential equation subject to specified initial conditions.

Integration Curve

The curve defining the solution of a differential equation.