課程名稱︰常微分方程導論
課程性質：數學系大二必修
課程教師︰林紹雄
開課學院：理學院
開課系所︰數學系
考試日期︰2010年12月28日(二)，14:30-17:20
考試時限：50分鐘
是否需發放獎勵金：是
試題 :
Math 201-24900 (ODE) Quiz No.7 (12/28/2010)
There are problems (A) to (D) with a total of 50 points. Please write down your
computational or proof steps clearly on the answer sheets.
Consider the following prey-predator system
dx 2 dy 2
---- = 30x - 2x - xy, ---- = 80y - 4y + 2xy.
dt dt
Answer the following questions.
A. (5 points) Which species is the prey?
B. (20 points) Find its equlibria, and discuss their type and stability.
C. (15 points) Draw its phase portrait which you think is the right picture in
the quadrant x≧0, y≧0.
D. (10 points) Let x(0)≧0, y(0)≧0. Must x(t) exist for all t≧0, and the
limit lim x(t) exist?
t→∞
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