Series solution methods 用來解非 constant coefficeints?

Definition of the Laplace transform | Lecture 29 | Differential Equations for Engineers

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See notes in Stochastic Processes Week 1.8.

之前是直接在 $t$-space 上找 solution. 另一種方式為先轉到 $s$-space, 然後找 solution 後轉回 $t$-space (這步是難的).

• 一些 funtion 何其對應的 Laplace transform 結果 (其中第 12 的 $u_c(t)$ 是 heaviside step function, see lecture 32)

The Laplace Transform of Sine

Compute the Laplace transform of $f(t)=\sin bt$

會使用到兩次 integration by parts

$$ \int_a^budv+\int_a^bvdu=\left.uv\right|_a^b $$

Laplace transform of a constant coefficient ode | Lecture 30 | Differential Equations for Engineers

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