Econ 142b/310b
Quiz 04
Instructor: Meng-Yu Liang
TA: Otto Reich
March 21, 2002
1. (2 point) Use the matrix method as in textbook to solve the following dierential-equation system:
x (t) + 6y (t) x(t) + 10y (t) = 2
y (t) + x(t) y (t)
= 10
(with x (0) = 0 a
Student Name:
Student ID:
Econ 142b/310b
Quiz 02-solution
Instructor: Meng-Yu Liang
February 7, 2002
TA: Otto Reich
1. Use the method taught in class to solve the Bernoulli equation
2 6 dy ? t 3 y = ty 3
dt
Answer: Step 1: Let z = y ?2 . Hence dz = ? 2y ?
Student Name:
Student ID:
Econ 142b/310b
Solution to Quiz 03
Instructor: Meng-Yu Liang
TA: Otto Reich
February 21, 2002
1. (1 point)
(a)
d cos
d
1
1
= ( sin ) 12 =
1
sin
2
2
(b) Show that cos 2 1 2 sin
cos 2 = cos ( + ) = cos cos sin sin = cos2 sin2 = 1
Econ 142b/310b
Solutions to Quiz 02
Instructor: Meng-Yu Liang
TA: Zafrul Siddique
February 6, 2003
1. Use the method 1 taught in class to solve the Bernoulli equation. (Need all the steps.)
2
dy
ty = ty 3
dt
Answer: Step 1: Multiplying y 3 , we have
2y 3
Student Name:
Student ID:
Econ 142b/310b
Quiz 04
Instructor: Meng-Yu Liang
TA: Zafrul Siddique
March 21, 2003
Note that x and y are functions of t and x =
dx
dt ,
y=
dy
dt .
1. (3 points) Draw the phase diagrams for the following questions. Then determine
Student Name:
Student ID:
Econ 142b/310b
Quiz 02
Instructor: Meng-Yu Liang
TA: Zafrul Siddique
February 6, 2003
1. Use the method 1 taught in class to solve the Bernoulli equation. (Need all the steps.)
2
dy
ty = ty 3
dt
1
2. Use the method 3 taught in c
Student Name:
Student ID:
Econ 142b/310b
Solutions to Quiz 03
Instructor: Meng-Yu Liang
TA: Zafrul Siddique
February 20, 2003
Note : If ax2 + bx + c = 0, then x =
b b2 4ac
2a
1. (2 points) Given y (0) = 1 and y (0) = 2, nd y (t) s.t.
y (t) + 5y (t) + 4y (