Systems of linear first-order odes | Lecture 39 | Differential Equations for Engineers

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我們有兩個 functions $x_1(t)$ and $x_2(t)$, 也有對應的兩個 first-order linear constant coefficients odes (homogeneous)

注意到這是 coupled ode: see https://youtu.be/9h1c8c29U9g?si=OAglG9Lo0vdEaFne&t=473

意思是我們無法單獨解某一條 first order ode, 必須所有的 odes 一起解.

這樣的 ode system 可以用 matrix form 來表達

使用猜測解為 $x(t)=ve^{\lambda t}$, 其中 $v$ is of dimension $2\times 1$ 的 column vector.

則我們發現就是在解 eigenvalue eigenvector problems

課程說只討論 distinct solutions, 因為 repeated solution 對現階段學 ode 來說太特殊了??

System of odes with distinct real eigenvalues | Lecture 40 | Differential Equations for Engineers

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其實滿簡單的… first order “coupled” linear ode with constant coefficients.

System of odes with complex eigenvalues | Lecture 41 | Differential Equations for Engineers

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