課程名稱︰工程數學一
課程性質︰必修
課程教師︰王昭男
開課學院：工學院
開課系所︰工程科學及海洋工程學系
考試日期（年月日）︰2009/10/29
考試時限（分鐘）：120分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
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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