MATHEMATICS FOR PART I ENGINEERING MA172/176
SEMESTER 2 EXAMINATION 2002/03
SECTION A
A1. (2 marks) Find an integrating factor for the dierential equation
dx x
+ = t2 .
dt
t
(Do NOT solve the equation).
A2. (2 marks) Show that the equation (x + sin t)
NOT
MATHEMATICS FOR PART I ENGINEERING MA171/172/176
SEMESTER 2 2001/02 SOLUTIONS
SECTION A
1. The integrating factor is exp
2. (x2 + t)
p
2t dt = exp(t2 )
dx
+ t2 + x = 0
dt
q
q
p
= 1,
= 1.
t
x
These partial derivatives are equal so the equation is exact.
d2
MATHEMATICS FOR PART I ENGINEERING MA172/176
SEMESTER 2 2002/03 SOLUTIONS
SECTION A
1. The integrating factor is exp
2. (x + sin t)
p
1
dt = exp(ln t) = t
t
dx
+ t2 + x cos t = 0
dt
q
q
p
= cos t,
= cos t.
t
x
These partial derivatives are equal so the eq
MATHEMATICS FOR PART I ENGINEERING MA176
SEMESTER 2 EXAMINATION 2000/01
SECTION A
1. Find an integrating factor for the dierential equation
the equation).
2. Determine whether the equation (2xt2 + x2 )
the equation).
dx x
= t2 . (Do NOT solve
dt
t
dx
+ 2
MATHEMATICS FOR PART I ENGINEERING MA176
SEMESTER 2 EXAMINATION 1999/2000
SECTION A
1. Find an integrating factor for the dierential equation
the equation).
2. Find the complementary function ONLY of
dx 2x
+
= t. (Do NOT solve
dt
t
dx
d2 x
5 + 4x = et .