# 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 LinearOrdinaryDifferentialEquation 2013-03-22 15:31:11 2013-03-22 15:31:11 matte (1858) matte (1858) 4 matte (1858) Definition msc 34-00 msc 35-00