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2. Solve for the following ordinary differential equation
(15%)

其他申論題

(2) 欲使溶液中 FeS 全部溶解，溶液的需高於多少 M？

第二大題英翻中(20%) 請將閱讀第一題的兩段內容翻成中文。

第三大題中翻英(20%) 此實驗以兩種珊瑚Isoporapollifera 與Poritob 進行不同程度酸化測試。想知道珊瑚身上微生物的多樣性指數Shannon index的差異。請根據下圖的結果英文描述此實驗結果。

1. Use the integrating factor method to solve the following ordinary differential equation.y'+y= (10%)

3. Use the undetermined coefficient method to solve the following ordinary differential equation y" + y = cos(x) (15%)

4. Use the Lagrange method (variation parameter method) to solve the same ordinary differential equation shown in problem 3. y" +y = cos(x) (15%)

5. Using the Laplace transform to solve the following initial value ordinary differential problem. y" + 8y'+ 16y = y(0) = 1, y'(0) =-4 (15%)

6. Use the Laplace transform to solve the following ordinary differential equation. y"+4y = f(t) y(0) =y'(0)=1

7. An elastic string of length L with fixed ends is released from rest (zero initial velocity) from an initial position given as a function of y = f(x). The initial- boundary value problem for the position function y(x,t) is Please solve for the function of the position function y(x, t) (15%)

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