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︰工程科學與海洋工程學系
考試日期（年月日）︰96/10/29
考試時限（分鐘）：120
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. A cylindrical tank 1.50 m high stands on its circular base of diameter
1.00 m and is initially filled with water. At the bottom of the tank
there is a hole of diameter 1.00cm , which is opened at some instant,
so that the water starts draning under the influence of gravity.
Find the height h(t) of the water in the tank at any time t.
Experiments show that water issues from a hole with velocity
v(t)=0.6*(2gh)^(0.5)
2
where g = 980 cm/sec the acceleration of the gravity at the surface of
the earth. (15%)
2. Solve the initial value problem (15%)
2 2
2sin(y) dx +xycos(y) dy = 0 y(2)= (π/2 )^0.5
3. Solve the linear differential equation (15%)
y'+y/x^2 = 2xe^(1/x)
4. Find the steady state current I(t) in the RLC-circuit in following
figure if E(t)= E0 cosWt (15%)
RLC 和電源串聯之圖
5. Solve the following non-homogeneous differential equation (15%)
y'''-5y''+8y'-4y=e^(2x)
6. Find the general solution of the following equation (15%)
y''+y=secx
7. Suppose that the streamlines of the flow are φ (x,y) =xy.
Find their orthogonal trajectories (equipotential lines). (10%)
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