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Ecu202engineering Mathematics Iv Question Paper

Ecu202engineering Mathematics Iv

Course:Bachelor Of Science In Electrical And Electronic Engineering

Institution: Kenyatta University question papers

Exam Year:2012

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2011/2012
SECOND SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR
OF SCIENCE (ELECTRICAL AND ELECTRONICS ENGINEERING)
ECU 202:
ENGINEERING MATHEMATICS IV

DATE: Tuesday, 10th April, 2012

TIME: 8.00 a.m. – 10.00 a.m.
------------------------------------------------------------------------------------------------------------
INSTRUCTIONS:
Answer question ONE and any other TWO.
Question One (30 marks)
1.
a)
Find the differential equation associated with the Primitive
2x
2x
2
? x
y ? c e ? c xe ? c e
and hence state the order and the degree of the
1
2
3
differential equation.

(6 marks)
b)
Solve the linear differential equation 4
3
?x
x y??4x y ? e given that
y? 1
? ? ? .
0

(6 marks)
c)
Find the orthogonal trajectories of the family of curves
y?x2 ? ?
1 ? cx where c is a parameter.

(6 marks)
d)
Solve the homogeneous differential equation 2
x dy ? y?x? y? dx ? .
0

(6 marks)
e)
Use the method of undetermined co-efficient to solve the differential
equation y ?? 4y??4y ? x sin 2 .
x

(6 marks)

Page 1 of 3

Question Two (20 marks)
2.
a)
Solve the differential equation

? 4x?4 2 2 4
x y ? y ?dx?4 3
x y dy ? 0 where y? ?
1 ? .
2

b)
Use separation of variables to solve the differential equation

? 2x?2x? ?1dy ? ? 3y?3 2y?3y? ?1dx where y?? ?1? .1

c)
Solve the d.e

? 3
D ?3D?2?y ? 0 given the initial condition

y?0? ? ,
0 ?
y ?0? ? 9 and y??0? ? .
0

Question Three (20 marks)
3.
a)
Solve the differential equation ? 4
D ?2 3
D ?7 2
D 18
? D?26?y ? 0 given

that one of the roots is -1 + I

(7 marks)

b)
Test for exactness and solve the differential equations
?2xyCos? 2x?? 2xy? ?1dx??Sin? 2x? 2
? x ? dy ? 0
(7 marks)
c)
Solve the d.e
dx ? ?1
2
? x ?cot y dy ? .
0

(6 marks)

Question Four (20 marks)
4.
a)
Solve the following d.e
dy

i)
?x? ?1
? y ? ex ?x? ?2
1

(5 marks)
dx

ii)
? 2x?5x?6?dy ? ? 2y? ?1 .
dx

(5 marks)

iii)
? 2
D ?3D? 2?y ? 0

(5 marks)

b)
Prove that
x
y ? c Sin x ?c is a solution to the d.e
1
2

?1?xcot x? y?? ?y
x ? y ? .
0

(5 marks)

Question Five (20 marks)
5.
a)
Show that y ?c ex ?c e2x ? x is a Primitive of y ??3 ?
y ?2y ? 2x?3 and
1
2

Page 2 of 3

find a particular solution if the function is a curve that passes through the
points ? ,
0 0? and ? ,
1 0?.
dx
dy

b)
Solve the d.e simultaneously
?
? 2x? y ? 0
dt
dt
dy

? 5x ? 3y ? 0
dt

c)
A body at a temperature of 50oF. If after 10 minutes, the temperature of
the body is 75oF. Find the time required for the body to reach a
temperature of 100oF.

Page 3 of 3

Ecu202engineering Mathematics Iv Question Paper

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