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ODE602S- ORDINARY DIFFERENTIAL EQUATIONS - JAN 2020 |
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NAMIBIA UNIVERSITY
OF SCIENCE AND TECHNOLOGY
FACULTY OF HEALTH AND APPLIED SCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: Bachelor of science ; Bachelor of science in Applied Mathematics and Statistics
QUALIFICATION CODE: 07BSOC; 07BAMS
LEVEL: 6
COURSE CODE: ODE602S
COURSE NAME: ORDINARY DIFFERENTIAL
EQUATIONS
SESSION: JANUARY 2020
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 100
SUPPLEMETARY/SECOND OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER
Dr A. S EEGUNJOBI
MODERATOR:
Dr I.K.O AJIBOLA
INSTRUCTIONS
1. Answer ALL the questions in the booklet provided.
2. Show clearly all the steps used in the calculations.
3. All written work must be done in blue or black ink and sketches must
be done in pencil.
PERMISSIBLE MATERIALS
1. Non-programmable calculator without a cover.
THIS QUESTION PAPER CONSISTS OF 3 PAGES (Including this front page)
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ODE 6028S
Ordinary Differential Equations
QUESTION 1 [ 30marks]
1. (a) Solve the following differential equations:
i.
y' (x) = e**9 + xe
January 2020
ii.
ydz(1 + 2°) tan~' rdy = 0
iii.
x’ ydzx — (x* + y*)dy = 0
(b) Determine the solution of the following differential equations:
y-xt+l
/
—
V(@) = Tyy-8
ii.
y'1(z) +=ay=ne 2
(6)
QUESTION 2 [25 marks]
2. (a) i. If y:(x) and yo(zx) are two solutions of second order homogeneous differential
equation of the form
where p(x) and g(x) are continuous on an open interval J, then show that
W(yi(2), Yyo(x)) = cen J P(a)dz
where c is a constant.
(6)
ii. Use reduction of order method to find yo(z) if
y”—6y+9=0; w(x) =e*
(b) Solve the following:
i.
ii.
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ODE 6025S
Ordinary Differential Equations
January 2020
QUESTION 3 [21 marks]
3. (a) Solve the Euler equation
62%y/"(v) + S0y/(2)
(2) =0,
v)=2,
¥()=2
(b) Solve the following differential equations by method of variation of parameters
y" (x) + y(x) = tana
(c) Solve the following differential equations by method of undetermined coefficient
y" (a) + 2y'(a) + 2y(x) = —e*(5a — 11), y(0) =—-1, y/(0) =—3
(8)
QUESTION 4 [25 marks]
4. (a) i. Solve using Laplace transform
y(t) — 2y'(t) + 2y(t) = cost,
y(0)=1, y'(0)=0
ii. If
find L{ f(t)}
iii. Compute
sint, if O<t<qa
t)=
~~
I) ‘; if t>q,
ce { ws 1 }
(b) Solve the following differential equation by using Laplace transform
y'(t)+y'(t) + y(t) =sint, y(0)=1, y'(0)=-1
End of Exam!