Differential Equations/Glossary

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Contents 1 A 2 B 3 C 4 D 5 E 6 F 7 G 8 H 9 I 10 J 11 K 12 L 13 M 14 N 15 O 16 P 17 Q 18 R 19 S 20 T 21 U 22 V 23 W 24 X 25 Y 26 Z

[edit] A

[edit] B

[edit] C

complementary function 

The solution to the related homogenous equation for a nonhomogenous equation

[edit] D

differential equation 

An equation with one or more derivatives in it. F(x,y,y',y'',y''',...)

[edit] E

[edit] F

first order equation 

Any equation with a first derivative in it, but no higher derivatives. F(x,y,y')

[edit] G

general solution 

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

[edit] H

homogenous equation 

Any equation that is equal to 0. In differential equations, its an equation p_n(x)y⁽ⁿ⁾ + p_{n − 1}(x)y^{(n − 1)} + ... + p₀(x)y = 0.

[edit] I

initial condition 

A value of a function or its erivative 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 .

[edit] J

[edit] K

[edit] 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 f₀(x) + f₁(x)y + f₂(x)y' + f₃(x)y'' + ...f_n(x)yⁿ. No terms for y or its derivatives may be raised to a power or placed inside a function such as sin or ln

[edit] M

[edit] N

nonhomogenous equation 

Any equation that is not equal to 0. In differential equations, its an equation p_n(x)y⁽ⁿ⁾ + p_{n − 1}(x)y^{(n − 1)} + ... + p₀(x)y = f(x), 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

[edit] O

O.D.E 

See ordinary differential equation.

order 

The highest derivative found in a differntial equations. First order equations only have y', second order equations have y' and y'', etc.

ordinary differential equation

Any differential equation that has normal derivatives only

[edit] 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.

[edit] Q

[edit] R

[edit] S

satisfy 

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. F(x,y,y',y'')

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.

[edit] T

[edit] U

[edit] V

[edit] W

[edit] X

[edit] Y

[edit] Z