Final Exam Paper For Those who are taking Degree Of Civil Engineering..Prepared By Universiti Malaysia Pahang

1. Universilti
Malaysia
PAHANG
E?€tslGrlrlnE i'irlirir,,:niJ*? i grui_&ll! tt
F'ACULTY OF'INDUSTRIAL SCIENCES & TECHNOLOGY
FINAL EXAMINATION
COURSE ORDINARY DIFFERENTIAL EQUATIONS
COURSE CODE BUM2133IBAM1023/BKU10 13
LECTURER RAHIMAH BINTI JUSOH @ AWANG
NAJIHAH BINTI MOHAMED
ZULKIIIBRI BIN ISMAIL@MUSTOF'A
ISKANDAR BIN WAINI
DATE 9 JANUARI2Ol2
DURATION 3 HOURS
SESSION/SEMESTER SESSION 2OTII2OI2 SEMESTER I
PROGRAMME CODE BAA/BAE/BEE/BEP/BFF/BFMIBKB/ BKC/
BKG/BMA/ BMB/BMF/BMIIBMM
INSTRUCTIONS TO CANDIDATES
1. This question paper consists of FIVE (5) questions. Answer ALL questions.
2. All answers to a new question should start on a new page.
3. All the calculations and assumptions must be clearly stated.
4. Candidates are not allowed to bring any material other than those allowed by
the invigilator into the examination room.
EXAMINATION REOUIREMENTS :
1. APPENDICES
DO NOT TT]RN THIS PAGE T]NTIL YOU ARE TOLD TO DO SO
This examination paper consists of SIX (6) printed pages including the front page.

2. ,-
CONFIDENTIAL BAA/BAE/BEE/B EP/BFF/BFMIBKB/BKC/BKG/BMA/BMB/
BMF/BMIIBMN4/I I 12I IBAM2B3IBAM1O23/BKU1O13
I
I
Y
Celsius) of the bodyyand tb{:!tg*rpggdgg3rr. If a body in air at lyC wilt cool
from 900Cto 600 C in one minute, evaluate its temperature at the end of 4 ilinutes.
Uilic:
ff - -k(e - surrounding)
_s.* - lc L - l- )
t /n-
(10 Marks)
*J*
la
QUESTTON 2
cv "-.p- {# * T" )
*T=
J
/,
"f
.6 Show that this differential equation is an exact equation. Find its solution.
z(.*,t;b..[f *t)at =o 2r.l
Ib>
)) 't (8 Marla)
bL1
Use linear method to solve .bu
6
;"
Qyt)'4
Y'+1= e'
x
:: (7 Marks)
i:r. ) v
QUE
Find the general solution of the differential equation
Yo -4Y' =t +3e-z'
by using the method of undetermined coefficient.
(9 Marks)

3. CONFIDENTIAL BAA/BAE/BEE/BEP/BFF/BFM/BKB/BKC/BKG/BMA/BMB/
BMF/BMI/BMI[/1 1 12I IBVVU2B3|BAM1023/8KU1013
--
(b) Fin(he particular solution of the differential equation
r
>-*
{ (fi,'1jr' +fiy =3xz +2tnx
which satisfies the initial conditions y =l and y' = 0 when x = 1'
(16 Marks)
QUESTION 4
using the First
Determine the Laplace transform of the following expression by
Shift Theorem and the Second Shift Theorem'
;-_--___ ".-.jI-*#*.-'*.s
./)
(4et' 2tl-b3'u(t -3)l
+- cos' t ..*' ,J
(8 Marks)
of the
Use the Convolution Theorem to find the inverse Laplace transform
following expression.
3s
(s2 +1)(s2 +4)
(8 Marks)
(c) solve the differential equation
Y"-6Y'+9Y =t2e3'
with the initial conditions /(0) = 2 and y'(0) = e .
(g N{a*k$
t,'
I
;, Ll
I 4,-
| ' , {7'
',/
. _,r,/r' ,/

4. CONFIDENTIAL BAA/BAE/BEE/BEPIBFF/BFM/BKB/BKC/BKG/BMA/BMBi
BMF/BMVBMIWI 112I IBIJM1I33IBAM1O23/BKU1O13
QTTESTION s
V
(a) A periodic tunction f(t) ir defined as
2, -7T <t <-tr
o, -t=,=;
2
/(')= I
-2.
'2 L.t..o
f (t) = f (t +2n)
(i) Sketch the graph of this periodic function over the interval l-Zn ,lnf .
(ii) Determine whether f@ keven or odd.
(iii) Find the Fourier series of f Q).
(10 Marks)
/.--
(b) We want to find the half-range cosine series representation of
f(t)=1-,, 0<t<L
22
(i) Sketch the graph of the periodic function.
(ii) Write down the equation of the periodic function.
(iii) Find the Fourier cosine series representation of the periodic function.
(15 Marks)
EtlD oF QUESTION PAPER