PlanetMath: linear ordinary differential equation

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linear ordinary differential equation

(Definition)

The following problem is a linear ordinary differential equation:

Let $A\colon I \to \mathbbmss{C}^{n\times n}$ be a known matrix. Find a matrix $x\colon I \to \mathbbmss{C}^{n\times n}$ (or vector $x\colon I \to \mathbbmss{C}^n$ ) such that

$\displaystyle x'$	$\displaystyle =$	$\displaystyle Ax,$
$\displaystyle x(0)$	$\displaystyle =$	$\displaystyle x_0,$

where

is a known initial value.

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Cross-references: vector, matrix
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This is version 1 of linear ordinary differential equation, born on 2005-10-01.
Object id is 7389, canonical name is LinearOrdinaryDifferentialEquation.
Accessed 2564 times total.

Classification:

AMS MSC:	34-00 (Ordinary differential equations :: General reference works )
	35-00 (Partial differential equations :: General reference works )

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