MTM TEST 3 12 - test PDF

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POLYTECHNIC OF NAMIBIA

http://www.polytechnic.edu.na

SCHOOL OF HEALTH AND APPLIED SCIENCES Private Bag 13388, Windhoek, Namibia Phone: +264 (61) 207 2780 +264 (61) 207 2142

Fax:

DEPARTMENT OF MATHEMATICS & STATISTICS

Programme

Bachelor of Engineering

Course

Engineering Mathematics 125

Course Code

MTM210S

Level

6

Date

18 October 2012

Duration

1 Hour and 30 minutes

Total Marks

51

Examiners

Mr. F N NDINODIVA

Moderator

Mr. B OBABUEKI

CONTINUOUS ASSESSMENT TEST 3 (1st opportunity)

Instructions/Information to candidates: 1. 2. 3. 4. 5.

Examination conditions apply at all times. NO books, notes or cell phones allowed. No borrowing or lending of any equipment or stationery. Use of a non-programmable pocket calculator is required. Answer all questions and number your solutions correctly. Only blue or black ink may be used for written work. Work in pencil will not be marked.

6. Correction fluid (Tippex) may not be used. 7. Untidy / illegible work will attract no marks. 8. Round all answers to three (3) decimal places, unless indicated otherwise in a question.

Question 1 [16 marks] 1.1

Analyze the nature of each of these ordinary differential equations

1.1 .1 ( y ' 4xy )2  2  ye x 1.1 .2 k (ut ) 7  1.2

2 u 2 u  x 2 y 2

Form a differential equation from the family of functions y  Ae4 x  e6 x

[4] [4]

[8]

Question 2 [20 marks] 2.1

Use the separable variable method to solve the following initial value problem to obtain a particular solution for p dp 1 p  p (1  ) , where a and L are constants and the initial value condition dt a L p(0)  p0 ;0  p0  L [15]

2.2

By using a special case of variable separation equation leading to homogeneous dy [5] (homogeneous solutions), solve ( x2  xy)  x2 y  y2 . dx

Question 3 [15] Use any suitable method to solve each of the following differential equations 3.1 3.2

 cos x

dy  y sin x  cos2 x dx

ex sin ydx  (2 y  ex cos y) dy  0

[6] [9]...