课程名称︰工程数学一 课程性质︰必修 课程教师︰王昭男 开课学院：工学院 开课系所︰工程科学及海洋工程学系 考试日期（年月日）︰2009/10/29 考试时限（分钟）：120分钟 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 1.Solve the equation：(20%) 2 3 y'+y/x=3x y 2.Consider an object that is falling under the influnece of gravity in a medium.This medium retards the downward motion of the object. The magnitude of tis retarding force is proportional to the square of the velocity. If we assume that the object begains its motion from rest,i.e.,v(0)=0 Find the velocity of the object in terms of time t and the terminal velocity.﹝Assume the mass of the object is m,the gravity is g and the proportional constant is α.﹞ (20%) 1 -1 〈hint：∫--------dx=tanh (x)〉 1-x^2 3.Find the general solution of the linear differential equation.(20%) y"+4y=secx 〈hint：∫sec(x)dx=ln│sec(x)+tan(x)│〉 4.Find the general solution of the following equation：(20%) 2 x y"-5xy'+8y=2lnx 5.Solve the following non-homogeneous differetial equatuon.(20%) 2x y'''-5y"+8y'-4y= e --

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