P2.7
The interconnection is invalid. In the middle branch, the value of the current
i must be =25 A, since the 25 A current source supplies current in this branch
in the direction opposite the direction of the current i . Therefore, the voltage
supplied b
P 1.8
n=
35106
1.60221019
P.1.10
q=
t
0
P.1.17
[a]
i dt =
t
0
= 2.18 1014
20cos(5000t)dt =
20
5000 sin(5000t)
p = v i = (3.75e1000t 3.75e2000t ) W
to nd maximum, let
dp
dt
=0t=
[b]
w=
0
P. 1.20
[a]
pdt =
ln2
1000
3.75
1000
= 693.15s
3.75
2000
= 1.875mJ
v
P 4.86
Find the Thevenin equivalent with respect to the terminals of R0
Open circuit voltage
(440 220) = 5ia 2ib 3ic
0 = 2ia + 10ib 1ic
ic = 0.5v
v = 2(ia ib )
solving
ib = 26.4A
vT H = 7ib = 184.8V
short circuit current
440 220 = 5ia 2isc 3ic
0 = 2ia + 3
The general solution of y + 4y/t = t5 for t > 0 is
(1) y (t) = ln t + c
(2) y (t) = t4 + c
(3) y (t) = t4 ln t + c
(4) y (t) = t5 + c t4
(5) y (t) = t5 /4 + c t4
The general solution of y + 4y/t = t5 for t > 0 is
(1) y (t) = ln t + c
(2) y (t) = t4 + c
(3
Wich of the following pairings of an adjective with a noun
makes sense?
(1) a mowed mother
(2) a continuous interval
(3) a dierentiable equation
(4) true numerical values
(5) none of the above
Wich of the following pairings of an adjective with a noun
mak
Water of salinity 3 [lb/gal] enters a tank containing 7 gallons
of saline solution at the rate of 2 [gal/min]. The wellstirred
saline solution leaves the tank at the same rate of 2 [gal/min].
Initially, at time t = 0, the solution in the tank contains 11
The FOODE
sin(xy ) dx + cos(xy ) dy = 0
is not exact. Which of the following is true?
(1) It has an integrating factor = (x).
(2) It has an integrating factor = (y ).
(3) Neither.
The FOODE
sin(xy ) dx + cos(xy ) dy = 0
is not exact. Which of the followin
Consider the SOLIVP
3 + t2
y ( t) +
y (t) + cos(t) y (t) = t ; y (1) = 2 , y (1) = 4 .
2
Let (t) denote its unique solution.
Compute (1). The answer is
(1) 7
(2) 7
(3) 5
(4) 5
(5) none of the above
Consider the SOLIVP
3 + t2
y ( t) +
y (t) + cos(t) y (t
Consider the SOLODE
2
y (t) + y (t) + q (t)y (t) = 0 .
t
()
Suppose you know that y1 (t) = t3 is a solution.
Then Reduction of Order provides another solution
y2 (t) =y1 (t)
y1 2 (t)e
p(t) dt
dt,
which, together with y1 , makes a Fundamental System.
Which
The solution of the CCSOLIVP y 4y + 13y = 0, y (0) = 1,
y (0) = 5 has the form y = Ret cos(t ).
What is value of the phase shift ?
(1) =
(2) = /2
(3) = /3
(4) = /4
(5) = /5
The solution of the CCSOLIVP y 4y + 13y = 0, y (0) = 1,
y (0) = 5 has the form y
Find a particular solution Y = A e4t of
y + y = 3e4t
by the Method of Undetermined Coecients.
(1) Y = 4 e4t
(2) Y = 3/17 e4t
(3) Y = 3/4 e4t
(4) Y = 16/3 e4t
(5) Y = 19/3 e4t
Find a particular solution Y = A e4t of
y + y = 3e4t
by the Method of Undetermin
The spring system
mu + 1/3 u + 1/5 u = 0 ,
is critically damped.
What is the mass m?
(1) 1
(2) 5/3
(3) 1/15
(4) 5/36
(5) 1/9
u(0) = 0 , u (0) = 1
The spring system
mu + 1/3 u + 1/5 u = 0 ,
u(0) = 0 , u (0) = 1
is critically damped.
What is the mass m?
(1)
n2 xn
?
What is the convergence radius of the power series
9n/2
n=1
(1) 3
(2)
(3) 9
(4) 1/9
(5) 1
n2 xn
?
What is the convergence radius of the power series
9n/2
n=1
(1) 3
(2)
(3) 9
(4) 1/9
(5) 1
The correct answer is (1). Explanation: By the ratio tes
Consider the SOLODE
(4 x2 )y + y cos(4x) + y sin(6x) = 0
at the base point x0 = 0, which is an ordinary point.
Which of the following estimates for the convergence radius
of a power series solution about x0 = 0 of this SOLODE is
sound?
(1) 2
(2) 8
(3) 12