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F'ACULTY OF'INDUSTRIAL SCIENCES & TECHNOLOGYFINAL EXAMINATION

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 bythe invigilator into the examination room.

EXAMINATION REOUIREMENTS :

1. APPENDICES

DO NOT TT]RN THIS PAGE T]NTIL YOU ARE TOLD TO DO SO

COURSE

COURSE CODE

LECTURER

DATE

DURATION

SESSION/SEMESTER

PROGRAMME CODE

ORDINARY DIFFERENTIAL EQUATIONS

BUM2133IBAM1023/BKU10 13

RAHIMAH BINTI JUSOH @ AWANGNAJIHAH BINTI MOHAMEDZULKIIIBRI BIN ISMAIL@MUSTOF'AISKANDAR BIN WAINI

9 JANUARI2Ol2

3 HOURS

SESSION 2OTII2OI2 SEMESTER I

BAA/BAE/BEE/BEP/BFF/BFMIBKB/ BKC/BKG/BMA/ BMB/BMF/BMIIBMM

This examination paper consists of SIX (6) printed pages including the front page.

,-

I

I

Y

CONFIDENTIAL BAA/BAE/BEE/B EP/BFF/BFMIBKB/BKC/BKG/BMA/BMB/BMF/BMIIBMN4/I I 12I IBAM2B3IBAM1O23/BKU1O13

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)

QUESTTON 2

t /n- \

- lc L \- l- )

"-.p- {# * T" )*T=

_s.**J*

lacv

(10 Marks)

2r.lIb>

)) 'tbL1

.bu

;"Qyt)'4

::i:r. ) v

6

(8 Marla)

(7 Marks)

(9 Marks)

Find the general solution of the differential equation

Yo -4Y' =t +3e-z'

by using the method of undetermined coefficient.

/,J

"f.6 Show that this differential equation is an exact equation. Find its solution.

z(.*,t;b..[f *t)at =o

Use linear method to solve

Y'+1= e'x

QUE

{

CONFIDENTIAL

QUESTION 4

(c)

--\(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'

BAA/BAE/BEE/BEP/BFF/BFM/BKB/BKC/BKG/BMA/BMB/BMF/BMI/BMI\[/1 1 12I IBV\VU2B3|BAM1023/8KU1013

(16 Marks)

I

I 4,- , {7'| ' ',/

\. _,r, ,//r'

Determine the Laplace transform of the following expression by using the First

Shift Theorem and the Second Shift Theorem'

;-_--___ ".-.jI-*#*.-'*.s./)( 4et' cos' 2tl-b3'u(t -3)l\\+- t ..*' ,J

(8 Marks)

Use the Convolution Theorem to find the inverse Laplace transform of the

following expression.

3s

(s2 +1)(s2 +4)

(8 Marks)

solve the differential equation

Y"-6Y'+9Y =t2e3'

with the initial conditions /(0) = 2 and y'(0) = e . \

(g N{a*k$

t,'

;, Ll

V

CONFIDENTIAL BAA/BAE/BEE/BEPIBFF/BFM/BKB/BKC/BKG/BMA/BMBiBMF/BMVBMIWI 112I IBIJM1I33IBAM1O23/BKU1O13

QTTESTION s

2, -7T <t <-tr2

/(')= I o, -t=,=;-2. L.t..o'2

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<L22(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)

(a) A periodic tunction f(t) ir defined as

EtlD oF QUESTION PAPER