linear ordinary differential equation

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

	$\displaystyle x^{\prime}$	$\displaystyle=$	$\displaystyle Ax,$
	$\displaystyle x(0)$	$\displaystyle=$	$\displaystyle x_{0},$

where $x_{0}$ is a known initial value.

Title	linear ordinary differential equation
Canonical name	LinearOrdinaryDifferentialEquation
Date of creation	2013-03-22 15:31:11
Last modified on	2013-03-22 15:31:11
Owner	matte (1858)
Last modified by	matte (1858)
Numerical id	4
Author	matte (1858)
Entry type	Definition
Classification	msc 34-00
Classification	msc 35-00