linear ordinary differential equation

The following problem is a linear ordinary differential equation:

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

$x^{\prime }$ $=$ $Ax,$

$x(0)$ $=$ $x_0,$

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