課程名稱︰工程數學二 課程性質︰土木系必修 課程教師︰何昊哲 開課學院：工學院 開課系所︰土木系 考試日期（年月日）︰2018/3/19 考試時限（分鐘）：三小時 線上考試，可以用Word打完上傳，或是手寫後拍照貼在Word裡上傳 試題 : Problem 1 Singular solution. An ODE may sometimes have an additional solution that cannot be obtained from the general solution and is then called a singular solution. The ODE y'^2 - xy' + y = 0 is of this kind. Show by differentiation and substitution that it has the general solution y = cx - c^2 and the singular solution y = x^2/4. Explain Fig. 6. Fig. 6. Particular solutions and singular solution in Problem 16 應該是直接抓課本習題，圖就是問題裡的方程式圖形 Problem 2 Harvesting renewable resources. Fishing. Suppose that the population y(t) of a certain kind of fish is given by the logistic equation(11), and fish are caught at a rate Hy proportional to y. Solve this so-called Schaefer model. Find the equilibrium solutions y1 and y2 (> 0) when H < A. The expression Y = Hy2 is called the equilibrium harvest or sustainable yield corresponding to H. Why? 線上考試...翻書看公式吧，不然怎麼寫 ------- 題目有錯字請推文或站內告知~ --

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