solutionofexam_2MTHMTH205

solutionofexam_2MTHMTH205 - Department of Mathematics and...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Department of Mathematics and Statistics American University of Sharjah Second Midterm Exam - Spring 2010 MTH 205 -- Differential Equation Date: April 14, 2010 Time: 5:00—6:15 pm Instructork Name: C. Alobaidi A. Sayfy Z. Abdulhadi Q '\ Student Name: Xx» Student ID Number: Time of the Lecture: M I . Do not open this exam until you are told to begin. 2. N0 Questions are allowed during the examination. 3. This exam has 5 questions. 4. Do not separate the pages of the exam. 5. Scientific calculator are allowed but cannot be shared. Graphing Calculators are not allowed. 6. Turn ofl all cell phones and remove all headphones. 7. Take ofl your cap. 8. No communication cfany kind. Student signature: ’ WM“ Q]. (35 points) Multiple Choices: Circle the correct answer. I. The existence and uniqueness theorem guarantees a unique solution to the IVP: xzy'+ x y’+-—I—-y=~/;, y(l)=2,y’(l)=l on: 5¢x x——3 (A) (‘5, 5) f (B) [0. 3] (C) (5, °°) \ (D), (0. 3) (E) (0, 5) \fV II. All the following pairs of functions are linearly independent on (~00, 00) ’ L/ exept: (A) 1, e“ (B) sinx, cosx (C) x, x2 e", eN3 (E) x, xe‘ 1 III. The period of the motion described by the equation a x’y + 18x = 0 is: (A) 3 35 (C) 5 (D) 6 (E) 1 2r 3 6 IV. The amplitude of the motion which is describe by the WP 2y'+8y = 0, y(0) = 0, y’(0) = 6 is: (A) 2 @3 (C) 4 (D) 6 (E) 8 V. The motion which is describe by the equation x'+ 2x’+ x = 0 is: (A) simple harmonic (B) overdamped (C) underdamped critically damped (E) beats VI. A fundamental set of solutions of y“) +4ym +4y"=0is: (A) 0, x, (2‘, e" (B) l, x, e'z" (C) 1, x, x2, e4" @ 1’ x’ 84'" “'2‘! (E) 1, 9“ VII. The form of a particular solution of ym+ '= 2 +003 2x is: (A) A + Bcost (B) A + Bsin x + Ccosx @ Ax + Bsin 2x + Ccost (D) Ar + Bxsin 2x + Crcos 2x (E) A): + 88in x «t» Coos x Q2. (15 points) Given that y, 2 e“ is a solution of the differential equation: xy'—(x+ l)y'+y =0, x>0. Use the reduction of order technique to find the general solution . bum ikawL “1‘2” 3 O ) 7C 7< ' i w '7<‘ %\ 1 87”" (AX Q3. (15 points) Use the method of undetermined coefficients to find the solution of the I.V.P. 2y'+4y'+2y=e‘+x , y(0)=1, y’(0)=0. <3 \NXW ‘WW i»; ,3 __ “W3 ,><~._.,2:, QC€7<% QALV LAC 6% +'ZA7L*1K+2C€ “C h §C%MC*ZCZ )C\ 8C:\~:‘>C‘:;] A) -l:~28 , WMNK Q4. (15 points) Use variation of parameter to find the general solution of the differential equation: xzf- 2y = x2 ./ ,. mg.“ / , .4; .—~. 7/ C) WW Om”2> W\?N Z [ww+\> :cg m "if, “ W _ C1 7;) VY’\ ,\ 74 + v ~ ’ l 75 01 >4 : L3 LMX l “' \ , 3 m 7< 2_ “‘7 M "1 * I, . \ O X ()1 x 71 M 6’} 7“”? 05. (20 points) A mass weighing 128 pounds stretches a spring 2 feet. The mass is initially released from a point 6 inches above the equilibrium position with no initial velocity and by simultaneously applying to the mass an external force F(t) ==85in(4t). Assuming no air resistance: 21) Find the initial value problem corresponding to motion of the spring. b) Solve the [VP in part (a) to find the motion of the mass. c) Find the position of the mass at t: It/ 43nd state whether it is below or above the equilibrium position. b0: W‘VCB 2) 3‘1 §‘1W\i31):>m39 e 3 \ Ribti g$fmbfif Li 7< ” 4i 6L} >< -.., <3 u t , 7m» : .. p mix 7i H l b : 1 jglfl Ll ‘QON’CQCQ U” W a a)» W“)??? \U hag/WE,“ ‘ EEK; {Ni ix 1 C\ (as; AV 3‘ <1, 3\NV’\W% ] l 74]”)12i/QlEJCl-M5iokfi‘)+(678’ I L ‘ Ell-tangents emu, 7<FltuLlfliSivxgarKAm A(QM A i Cagtflt] + gen/m; . //; 53t~lbiwflq ii ...
View Full Document

This note was uploaded on 02/12/2012 for the course MTH 205 taught by Professor Sadik during the Spring '11 term at American Dubai.

Page1 / 7

solutionofexam_2MTHMTH205 - Department of Mathematics and...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online