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Homelinear ordinary differential equation

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# 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.

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## Mathematics Subject Classification

34-00*no label found*35-00

*no label found*

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