Universilti                                     Malaysia                                     PAHANG                       ...
,-      CONFIDENTIAL                                     BAA/BAE/BEE/B EP/BFF/BFMIBKB/BKC/BKG/BMA/BMB/                    ...
CONFIDENTIAL                            BAA/BAE/BEE/BEP/BFF/BFM/BKB/BKC/BKG/BMA/BMB/                                      ...
CONFIDENTIAL                          BAA/BAE/BEE/BEPIBFF/BFM/BKB/BKC/BKG/BMA/BMBi                                        ...
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BUM 2133 ORDINARY DIFFERRENTIAL EQUATIONS FINAL EXAM PAPER

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

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BUM 2133 ORDINARY DIFFERRENTIAL EQUATIONS FINAL EXAM PAPER

  1. 1. Universilti Malaysia PAHANG E?€tslGrlrlnE iirlirir,,:niJ*? i grui_&ll! tt FACULTY OFINDUSTRIAL SCIENCES & TECHNOLOGY FINAL EXAMINATIONCOURSE ORDINARY DIFFERENTIAL EQUATIONSCOURSE CODE BUM2133IBAM1023/BKU10 13LECTURER RAHIMAH BINTI JUSOH @ AWANG NAJIHAH BINTI MOHAMED ZULKIIIBRI BIN ISMAIL@MUSTOFA 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/BMIIBMMINSTRUCTIONS 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. 2. ,- CONFIDENTIAL BAA/BAE/BEE/B EP/BFF/BFMIBKB/BKC/BKG/BMA/BMB/ BMF/BMIIBMN4/I I 12I IBAM2B3IBAM1O23/BKU1O13IIY 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. 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-b3u(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. 4. CONFIDENTIAL BAA/BAE/BEE/BEPIBFF/BFM/BKB/BKC/BKG/BMA/BMBi BMF/BMVBMIWI 112I IBIJM1I33IBAM1O23/BKU1O13 QTTESTION sV (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

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