課程名稱︰工程數學
課程性質︰系定必修
課程教師︰林俊男
開課學院：
開課系所︰生工系
考試日期（年月日）︰96/11/07
考試時限（分鐘）：110
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
工程數學(一)2007/11/07
學號_____________________姓名______________________
注意事項：(1)公平起見，不得使用計算機
(2)可利用答案紙之右半邊作為計算用紙
(3)試題紙及答案紙請寫明學號及姓名一齊交回
(4)考試時間：10:20~12:10。每題15分共105分。
1.Find the general solutions (real function) of the following ordinary
equations.
2
2xydx + (4y + 3x )dy = 0 (integrating factor : f(y))
2.Find the general solutions (real function) of the following ordinary
equations.
2 2
(x + 3y )dx - 2xydy = 0
3.Find the general solutions (real function) of the following ordinary
equations.
2 4
3xdy/dx + y +x y = 0
4.Find the general solutions (real function) of the following ordinary
equations.
4 4 3 3 3 2 2 2
3xd y/dx + 22x d y/dx +38x d y/dx + 12xdy/dx = 0
5.Find the general solutions (real function) of the following ordinary
equations.
2 2 -1 x
2d y/dx - 4dy/dx +2y = x e + cosx
6.Find the general solutions (real function) of the following ordinary
equations.
4 4 2 2 2
d y/dx - d y/dx =3x -sin2x
7.試求與下所之列曲線族，互相垂直之曲線族
1/2
x = cy
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