Ordinary Differential Equations/Glossary

AEdit

BEdit

CEdit

complementary function
The solution to the related homogenous equation for a nonhomogenous equation

DEdit

differential equation
An equation with one or more derivatives in it.  
domain
a solution of differential equation is a function y=(x)y which, when substituted along with its derivative among the differential equation satisfies the equation from all x in some specified interval.

EEdit

FEdit

first order equation
Any equation with a first derivative in it, but no higher derivatives.  

GEdit

general solution
The solution to a differential equation in its most general form, constants included

HEdit

homogenous equation
Any equation that is equal to 0. In differential equations, its an equation  .

IEdit

initial condition
A value of a function or its derivative at a particular point, used to determine the value of constants for a particular solution
initial value problem
A combination of a differential equation and an initial condition. An initial value problem is solved for a total solution including the value of all constants
integration factor
A factor a differential equation is multiplied by to discover a solution .

JEdit

KEdit

LEdit

linear equation
An equation who's terms are a linear combination of a variable and its derivatives. Such an equation is in the form  . No terms for y or its derivatives may be raised to a power or placed inside a function such as sin or ln

MEdit

NEdit

nonhomogenous equation
Any equation that is not equal to 0. In differential equations, its an equation  , where f(x) is not 0.
non-linear equation
Any equation that is not a linear combination of a variable and its derivatives. Either one of the terms has the variable taken to a power, or is in a function such as sin or ln

OEdit

O.D.E
See ordinary differential equation.
order
The highest derivative found in a differential equations. First order equations only have  , second order equations have   and  , etc.
ordinary differential equation
Any differential equation that has normal derivatives only

PEdit

partial differential equation
Any differential equation that has partial derivatives in it
particular solution
A solution to a differential equation with all constants evaluated
P.D.E
See partial differential equation.

QEdit

REdit

SEdit

satisfy
to solve a differential equation. Used as an adjective, a solution to a differential equation satisfies that equation
second order equation
Any equation with a second derivative in it, but no higher derivatives.  
separable equation
An equation where the x and y terms are multiplied and not added.  
substitution method
A method of turning a non-separable equation into a separable one.

TEdit

UEdit

VEdit

WEdit

XEdit

YEdit

ZEdit