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ODE602S - ODINARY DIFFERENTIAL EQUATIONS -1ST OPP - NOVEMBER 2024 |
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F
nAmlBIA UnlVERSITY
OF SCIEnCEAno TECHnOLOGY
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ResourceasndApplied
Sciences
Schoool f NaturalandApplied
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Departmentof Mathematics,
Statisticsand Actuarial Science
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QUALIFICATIONS: BACHELOR of SCIENCE IN APPLIED MATHEMATICS AND STATISTICS
AND BACHELOR OF SCIENCE
QUALIFICATIONCODES: 07BSAM, 07BSOC
LEVEL:6
COURSE:ORDINARY DIFFERENTIAL EQUATIONS
DATE: NOVEMBER 2024
DURATION: 3 HOURS
COURSECODE: ODE602S
SESSION: 1
MARKS: 100
EXAMINER:
MODERATOR:
FIRST OPPORTUNITY: QUESTION PAPER
Prof Adetayo 5. Eegunjobi
Prof Sunday A. Reju
INSTRUCTIONS:
1. Answer ANY FOUR (4) 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 3 pages including this front page
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ODE 602S
Ordinary Differential Equations
November 2024
1. Discuss the existence and uniqueness of the following two IVPs and solve them.
(a) = y2 (x) - 1, y(0) = 0
(7)
(b) 4y'(x) = y½, y(0) = 0
(7)
(c) Solve
y - xy'(x) = yy'(x) + x
(11)
2. (a) The solutions of second order homogeneous differential equation of the form
y"(x) + p(x)y'(x) + q(x)y(x) = f(x)
are y1 and y2 where p(x) and q(x) are continuous on an open interval I, find the
formula for u(x) and v(x) of the particular solution by using variation of parameters.
(7)
(b) Find Y2(x) for all values of x if Y1(x) = ex W(y1, Y2)= ex(x2 - 2) Y2(l) = 3
(8)
(c) Find the general solution of x2y"(x) - 2xy'(x) + 2y(x) = x4ex by using variation of
parameter method
( 10)
3. (a) Solve y'(x)-y(x)tanx = -y(x)2secx
(9)
(b) Find the general solution of y'(x) = 1 + (y - x)2, y1 (x) = x
(8)
(c) The quantity N (t) of bacteria in a culture increased at a rate proportional to N (t).
The value of N(t) was initially 100 and rose to 332 in one hour. What was the
! value of N(t) after hours?
(8)
4. (a) Using shifting with multiplication theorems, find the Laplace transform of t2e-st sin t.
(8)
(b) Evaluate
(7)
(c) Find
1.
(5)
ii.
(5)
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ODE 602S
Ordinary Differential Equations
November 2024
5. (a) Use Laplace transform to find y"(t)+2y'(t)+5y(t) = e-tsint, y(0) = 0, y'(0) =
1
(8)
(b) Find the general solution of y"(x) + 6y'(x) + 9y(x) = 9x + 6
(7)
(c) Solve xy'(x) + y(x) = x4y3 (x)
(10)
End of Exam!