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Eem 207:Mathematics For Engineers Iii Question Paper

Eem 207:Mathematics For Engineers Iii

Course:Bachelor Of Science

Institution: Kenyatta University question papers

Exam Year:2011

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KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2011/2012
FIRST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF
SCIENCE (ENGINEERING)

EMM 207: MATHEMATICS FOR ENGINEERING III
DATE:
Thursday 15th December 2011 TIME:
2.00p.m – 4.00p.m
INSTRUCTIONS
Answer question ONE and any other TWO
Question One (COMPULSORY) 30 Marks
a) Form the differential equation from the following primitive equation and hence
state the order and degree of each differential equation
i)

[3marks]
ii)

[4marks]
b) Solve the 1st order differential equations(
) (
) [5marks]

c) If
/

/

/ is
the maximum value.

[5marks]
d) The rate of which a body cools is proportional to the difference between the
temperature of the body and that of the surrounding air. If a body in air at 25oC
will cools from 100o C to 75o in one minute, determine its temperature at the end
of three minutes.

[6marks]
e) Solve the initial value problem

for y(o) = 1 and
y’(o) = 1.

Using Laplace Transform.

[6marks]
Question Two (20 marks)
a) Solve the homogeneous differential equation /
/ .

[4marks]
Page 1 of 3

b) Test for exactness in the d.e (

)
(

)

[5marks]
c) Solve the Bernoulli equations

/

[6marks]
d) Uranium disintegrates at a rate proportional to the amount present at any instant.
If M1, and M2 grams of uranium are present at time t1 and t2 respectively show
that the half-life of uranium is ( )

[5marks]

Question three (20marks)
a) Solve the following differential equation
i)

[5marks]
ii)
)

[5marks]
iii)

/

[5marks]
b) Solve the equation

where L, R and Eo are constants.

[5marks]
Question four ( 20marks)
a) Test for exactness in the differential equation and hence solve it
(
)

[5marks]
b) i)
Define Laplace transform of f(t).

[2marks]
iii)
Find the Laplace transform of
( ) { /

[3marks]

c) Find the inverse Laplace transform of ( )

[4marks]
( )
d) Using Laplace transform technique solve the initial value problem

for y (o) = = 0.

[6marks]

Question five (20marks)
a) Differentiate between the following terms as used in differential equations
i)
Particular solution and general solution.

[3marks]
ii)
Order and degree

[2marks]
b) Classify the following differential equation into its order and degree.
v

[4marks]
c) A mechanical system with two degree of freedom satisfies the equation

+ = 4 and

- = 0

Page 2 of 3

Obtain an expression for x and y in terms of t given x, ,
/ vanish at t =

0.

[5marks]
d) Determine the particular solution of the differential equation

for y (2) = 1.

[6marks]
Page 3 of 3

Eem 207:Mathematics For Engineers Iii Question Paper

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