# linear ordinary differential equation

The following problem is a *linear ordinary differential equation ^{}*:

Let $A:I\to {\u2102}^{n\times n}$ be a known matrix. Find a matrix $x:I\to {\u2102}^{n\times n}$ (or vector $x:I\to {\u2102}^{n}$) 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 |