Ordinary Differential Equations/Glossary
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- complementary function
- The solution to the related homogenous equation for a nonhomogenous equation
- differential 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.
- general solution
- The solution to a differential equation in its most general form, constants included
- homogenous equation
- Any equation that is equal to 0. In differential equations, its an equation .
- 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 .
- 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
- 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
- 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
- particular solution
- 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.
- 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.