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