Assignment 5 for MAT3270A
October 6,2016
Section 3.5; P184:2,4,6,8,10
In each of the following problems, find the general solution of the
given differential equation.
2. y 00 + 2y 0 + 5y = 4 sin 2t
4. y 00 + y 0 6y = 18e3t + 12e2t
6. y 00 + 2y 0 = 5 + 4 s

Sample Solutions of Assignment 1 for MATH3270A
a
Note: Any problems about the sample solutions, please email Ms.Zhang Rong (rzhang
math.cuhk.edu.hk) directly.
Section 2.1
13. y 0 y = 4te2t , y(0) = 1.
Answer: Multiplying the ODE by et , we obtain
d
(yet )

Assignment 7 for MAT3270A
October 20, 2016
Section 4.4
P244: 3,13
In the following problem, use the method of variation of parameters to determine the general
solution of the given differential equation.
3. y 000 2y 00 y 0 + 2y = e5t
13. Given that x, x2

Assignment 6 for MAT3270A
October 13,2016
Section 4.1; P227:20; P228:26,27,28
20.In this problem we show how to generalize Theorem3.2.7(Abels theorem) to higher order
equations. We first outline the procedure for the third order equation
000
00
0
y + p1 (

76
Chapter 2. First Order Difkmnlial Equatiln
3. The possible points of discontinuity, or singularities, of the solution can be identied
(without solving the problem) merely by nding the points of discontinuity of the coef
cients. Thus, if the coefcient

Sample Solutions of Assignment 2 for MATH3270A
a
Note: Any problems about the sample solutions, please email Ms.Zhang Rong (rzhang
math.cuhk.edu.hk) directly.
Section 2.4
In each of the following problems, determine (without solving the problem) an interv

Sample Solutions of Assignment 4 for MAT3270A
Note: Any problems to the sample solutions, please email Ms. Zhang Rong
a
(rzhangmath.cuhk.edu.hk)
directly.
Section 3.4; P172: 1-6; P174:23-26
In each of the following problems, find the general solution of t

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Sample Solutions of Assignment 7 for MATH3270A
a
Email Miss ZHANG Rong(rzhangmath.cuhk.edu.hk)
directly if you have any questions on the
sample solutions.
Section 4.4
P244: 3,13
In the following problem, use the method of variation of parameters to determ

Correction
This note is the correction of the part Check linearly independent of solutions in Case I&Case
II on page 6&7 of Lecture note 12.
The desired conclusion of linearly independent is a direct corollary of the following general
result:
Proposition

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Assignment 4 for MAT3270A
September 29,2016
Section 3.4; P172: 1-6; P174:23-26
In each of the following problems, find the general solution of the
given differential equation.
1. y 00 + 2y 0 + y = 0
2. 9y 00 + 12y 0 + 4y = 0
3. 4y 00 8y 0 5y = 0
4. 4y 00

Assignment 3 for MAT3270A
September 22,2016
Section 3.1; P144: 1, 3, 5, 7
In each of the following problems, find the general solution of the
given differential equation.
(1). y 00 + 3y 0 4y = 0
(3). 12y 00 y 0 y = 0
(5). y 00 + 6y 0 = 0
(7). y 00 8y 0 +

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Sample Solutions for Assignment 3 for MAT3270A
Note: Any questions about the sample solution, please email Ms.Zhang Rong
(rzhang@math.cuhk.edu.hk) directly.
P144: 1, 3, 5, 7
In each of the following problems, find the general solution of the given differe

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Sample Solutions of Assignment 6 for MAT3270A
Note: Any problems to the sample solutions, please email Miss ZHANG Rong
a
(rzhangmath.cuhk.edu.hk)
directly.
Section 4.1; P227:20; P228:26,27,28
20.In this problem we show how to generalize Theorem3.2.7(Abels