首頁 > 線上測驗 > 100年研究所工程數學歷屆試題(工數1)電機所.電子所. 電信所.光電所.通訊所(二年期) > 100年國立暨南大學電機所電子組工程數學
Which is the solution of y´= 1+ y2 ?
arc tan y = x + 2
y = tan(x + 3)
y = tan x + 2
y = cos x + 2
y = tan x
Which the given functions are linear independent?
cos x, sin x
ex , xex
x1.5 , x0.5
ln x, (ln x2 ), (ln x)2
x2 , x | x |, x
Which is the Integrating Factor of the non-exact ODE: −ydx + xdy = 0 ?
x
x−1
y−2
(xy)−1
(x2 + y2 )−1
Which is the solution of y´´´+ y´´−y´−y= 0 ?
ex
ex + e−x
xex + e−x
xex + xe−x
ex + e−x + xex + xe−x
If f(x) = x3 + x ; for 0 < x < 2 , we are going to expand f(x) to Cosine series,
Sine series and Fourier series. Choose the correct converges value for different
series?
f(2) = 10 for Sine series
f(2) = 10 for Cosine series
f(2) = 5 for Fourier series
f(−1) = 2 for Sine series
f(−1) = 2 for Fourier series
A differential equation for unknown function y(x)
y´´+ 4y = 0
(1) Find the general solution for y(x) .
(2) Use Laplace Transform Method to find the general solution for y(x) .
(3) Use Power Series Method to find the general solution for y(x) .
(4) Are the answers obtained from (1), (2), and (3) the same?
Find the current i(t) in the RC circuit in the following Figure.
A voltage E(t) is applied. Assume charge and current is zero at t = 0
(Resistance = R , Capacitance = C ) [Use R, C, v0 , a, b, and t to express the answer]
(1) If applied voltage E(t) = V0 for t > 0 , Find the current i(t) .
(2) If E(t) = 0 for t < a ( a is positive), and E(t) = V0 for t > a ; Find the
current i(t) .
(3) If E(t) = V0 for a < t < b ( a, b are positive) and E(t) = 0 for otherwise; Find
the current i(t) .
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