# Linear differential equation

- Linear differential equation
- Linear Lin"e*ar (l[i^]n"[-e]*[~e]r), a. [L. linearis,
linearius, fr. linea line: cf. F. lin['e]aire. See 3d
{Line}.]
1. Of or pertaining to a line; consisting of lines; in a
straight direction; lineal.
[1913 Webster]

2. (Bot.) Like a line; narrow; of the same breadth
throughout, except at the extremities; as, a linear leaf.
[1913 Webster]

3. Thinking in a step-by-step analytical and logical fashion;
contrasted with {holistic}, i.e. thinking in terms of
complex interrelated patterns; as, linear thinkers.
[PJC]

Linear thinkers concluded that by taking the world
apart, the actions of people were more predictable
and controllable. --David Morris
(Conference
presentation,
Fairfield
University,
October 31,
1997)

{Linear differential equation} (Math.), an equation which is
of the first degree, when the expression which is equated
to zero is regarded as a function of the dependent
variable and its differential coefficients.

{Linear equation} (Math.), an equation of the first degree
between two variables; -- so called because every such
equation may be considered as representing a right line.

{Linear measure}, the measurement of length.

{Linear numbers} (Math.), such numbers as have relation to
length only: such is a number which represents one side of
a plane figure. If the plane figure is square, the linear
figure is called a root.

{Linear problem} (Geom.), a problem which may be solved
geometrically by the use of right lines alone.

{Linear transformation} (Alg.), a change of variables where
each variable is replaced by a function of the first
degree in the new variable.
[1913 Webster]

*The Collaborative International Dictionary of English.
2000.*

### Look at other dictionaries:

**Linear differential equation** — In mathematics, a linear differential equation is a differential equation of the form: Ly = f ,where the differential operator L is a linear operator, y is the unknown function, and the right hand side fnof; is a given function (called the source … Wikipedia

**linear differential equation** — noun : an equation of the first degree only in respect to the dependent variable or variables and their derivatives * * * Math. an equation involving derivatives in which the dependent variables and all derivatives appearing in the equation are… … Useful english dictionary

**linear differential equation** — Math. an equation involving derivatives in which the dependent variables and all derivatives appearing in the equation are raised to the first power. [1885 90] * * * … Universalium

**Differential equation** — Not to be confused with Difference equation. Visualization of heat transfer in a pump casing, created by solving the heat equation. Heat is being generated internally in the casing and being cooled at the boundary, providing a steady state… … Wikipedia

**differential equation** — Math. an equation involving differentials or derivatives. [1755 65] * * * Mathematical statement that contains one or more derivatives. It states a relationship involving the rates of change of continuously changing quantities modeled by… … Universalium

**Ordinary differential equation** — In mathematics, an ordinary differential equation (or ODE) is a relation that contains functions of only one independent variable, and one or more of their derivatives with respect to that variable. A simple example is Newton s second law of… … Wikipedia

**Matrix differential equation** — A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and of its derivatives of various orders. A matrix differential equation is one containing more… … Wikipedia

**Partial differential equation** — A visualisation of a solution to the heat equation on a two dimensional plane In mathematics, partial differential equations (PDE) are a type of differential equation, i.e., a relation involving an unknown function (or functions) of several… … Wikipedia

**Hypergeometric differential equation** — In mathematics, the hypergeometric differential equation is a second order linear ordinary differential equation (ODE) whose solutions are given by the classical hypergeometric series. Every second order linear ODE with three regular singular… … Wikipedia

**Delay differential equation** — In mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. A general form of the… … Wikipedia