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高階線性 O.D.E.

高階線性 O.D.E. 謝承道. 非線性. 齊次. 常係數. 線性. 非齊次. 變係數. 2-1 簡介. 高階 O.D.E. ( 尤拉 - 柯西方程式 ). 常係數線性 O.D.E. 二階線性 O.D.E. 齊次. n 階線性 O.D.E. 若 a 2 ( x ) 、 a 1 ( x ) 、 a 0 ( x ) 皆為常數. 若 r ( x ) = 0. 微分運算子. Ex ：. 齊次. 解. 非齊次. 解. 線性 O.D.E. 的解. y 1 ( x ) 、 y 2 ( x )…. y n ( x ) 為線性獨立. 特解. 齊次解.

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高階線性 O.D.E.

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  1. 高階線性O.D.E. 謝承道

  2. 非線性 齊次 常係數 線性 非齊次 變係數 2-1 簡介 高階O.D.E. (尤拉-柯西方程式)

  3. 常係數線性O.D.E. 二階線性O.D.E 齊次 n階線性O.D.E. 若a2(x)、a1(x)、a0(x)皆為常數 若r(x) = 0

  4. 微分運算子

  5. Ex：

  6. 齊次 解 非齊次 解 線性O.D.E.的解 y1(x)、y2(x)….yn(x)為線性獨立 特解 齊次解

  7. y1(x)、y2(x)….yn(x)為線性獨立 Wronskian 行列式 定義： 性質：

  8. 線性獨立 例7 請判斷y1、y2是否線性獨立？ (b) (a) Sol： (a)

  9. 線性相依 (b)

  10. 線性相依 Ex：請判斷y1、y2 、y3是否線性獨立？ Sol：

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