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ODE602S - PDINARY DIFFERENTIAL EQUATIONS - 2ND OPP - JANUARY 2025 |
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n Am I BI A u ni VE Rs ITY
OF SCIEnCE
FacultyofHealthN, atural
ResourceasndApplied
Sciences
Schoool f NaturalandApplied
Sciences
Department of Mathematics,
Statistics and Actuarial Science
13JacksonKaujeuaStreet
Private Bag13388
Windhoek
NAMIBIA
T: +264612072913
E: msas@nust.na
W: www.nust.na
QUALIFICATIONS: BACHELOR of SCIENCE IN APPLIED MATHEMATICS AND STATISTICS
AND BACHELOR OF SCIENCE
QUALIFICATION CODES: 07BSAM, 07BSOC
LEVEL:6
COURSE:ORDINARY DIFFERENTIAL EQUATIONS
COURSECODE: ODE602S
DATE: JANUARY 2025
SESSION: 1
DURATION: 3 HOURS
MARKS: 100
SECOND OPPORTUNITY/ SUPPLEMENTARY: EXAMINATION QUESTION PAPER
EXAMINER:
MODERATOR:
Prof Adetayo S. Eegunjobi
Prof Sunday A. Reju
INSTRUCTIONS:
1. Answer ALL questions on the separate answer sheet.
2. Please write neatly and legibly.
3. Do not use the left side margin of the exam paper. This must be allowed for the
examiner.
4. No books, notes and other additional aids are allowed.
5. Mark all answers clearly with their respective question numbers.
PERMISSIBLE MATERIALS
1. Non-Programmable Calculator
ATTACHEMENTS
1. None
This paper consists of 2 pages including this front page
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ODE 602S
Ordinary Differential Equations
1. Solve the following ordinary differential equations
(a) 2(x - y) + y'(x) = (y - (x + 1))2, y1(x) = x
(b) xdy + (y - x3y6)dx = 0
(c) By variation of parameter x 2y"(x) + xy'(x) - y(x) = lnx
January 2025
(9)
(9)
(9)
2. (a) Solve the initial-value problem by using the power series method and obtian the
first six terms (x2 + l)y"(x) + 2xy'(x) = 0, y(0) = 0, y'(0) = 1
(15)
! (b) Find the general solution of x 2y"(x) +xy'(x) + (x2 - )y(x) = 0 by using Frobenius
method at about x = 0.
(15)
3. (a) Use convolution theorem to find the inverse transform of
s
(s2 + l)(s 2 + 4) ·
(7)
(b) Find the following Laplace transform
£{cost cos 2t cos 3t}
(8)
(c) Find
(8)
4. (a) Solve the following using Laplace Transform
x'(t) -y(t) = et, y'(t) + x(t) = sint, x(0) = 1, y(0) = 0
(10)
(b) Find
£, 1 { 3s + 8 }
s2 + 2s + 5
(10)
End of Exam!
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