课程名称︰工程数学(ㄧ) 课程性质︰生工系必修 课程教师︰范致豪 开课学院：生农学院 开课系所︰生工系 考试日期（年月日）︰2015/10/14 考试时限（分钟）：60 试题 : 1. Test for exactness,If exact,solve.If not,use an integrating factor 2 (a) 2xydx+x dy=0 (10%) (b) sinxcosydx+cosxsinydy=0 (10%) 2. In a room containing 20,000ft^3 of air,600ft^3 of fresh air flows in per minute,and the mixture (made practically uniform by circulating fans) is exhausted at a rate of 600 cubic feet per minute(cfm). (a) What is the amount of fresh air y(t) at any time if y(0)=0 (10%) (b) After what time will 90% of the air be fresh? (15%) 3. Find the general solution.If an intial condition is given,find also the particular solution . (a) y'+ ysinx =e^(cosx) ,y(0)=-2.5 (10%) (b) xy' +4y =8x^4 ,y(1)=2 (15%) 4. A radioactive material decomposed at a rate proportional to the amount present.Suppose that the proportional constant is k=-1.5x10^(-11) 1/sec for the radioactive substance contained in the nuclear waste of our nuclear power plants .How many years will it take for this substance to decompose to 1/2 of its original quantity? (25%) (hint:背面附积分公式) -- 约1秒前 收回赞 留言 --

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