Ordinary Differential Equations/Glossary <
Ordinary Differential Equations
The solution to the related homogenous equation for a nonhomogenous equation
An equation with one or more derivatives in it.
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.
first order equation
Any equation with a first derivative in it, but no higher derivatives.
The solution to a differential equation in its most general form, constants included
Any equation that is equal to 0. In differential equations, its an equation
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
A factor a differential equation is multiplied by to discover a solution .
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
Any equation that is not equal to 0. In differential equations, its an equation
, where f(x) is not 0.
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
See ordinary differential equation.
The highest derivative found in a differntial equations. First order equations only have
, second order equations have and , etc. ordinary differential equation
Any differential equation that has normal derivatives only
partial differential equation
Any differential equation that has partial derivatives in it
A solution to a differential equation with all constants evaluated
See partial differential equation.
to solve a differential equation. Used as an adjective, a solution to a differential equation satisifes that equation
second order equation
Any equation with a second derivative in it, but no higher derivatives.
An equation where the x and y terms are multiplied and not added.
A method of turning a non-separable equation into a separable one.