Ordinary Differential Equations/Glossary

A B C complementary function The solution to the related homogenous equation for a nonhomogenous equation D 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. E F first order equation Any equation with a first derivative in it, but no higher derivatives. G general solution The solution to a differential equation in its most general form, constants included H homogenous equation Any equation that is equal to 0. In differential equations, its an equation . I 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 . J K L 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 M N 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 O 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 P 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. Q R S 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. T U V W X Y Z