课程名称︰工程数学二
课程性质︰土木系必修
课程教师︰何昊哲
开课学院：工学院
开课系所︰土木系
考试日期（年月日）︰2018/3/19
考试时限（分钟）：三小时
线上考试，可以用Word打完上传，或是手写后拍照贴在Word里上传
试题 :
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
应该是直接抓课本习题，图就是问题里的方程式图形
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?
线上考试...翻书看公式吧，不然怎么写