ORDINARY DIFFERENTIAL EQUATIONS WITH APPLICATIONS

(1) A cold beer with an initial temperature of
1
35 F
warms up to
40 F
in
10 minutes while sitting in a room of temperature
70 F
.

(i) What will be the temperature of the coke after t mins? Please
show details of calculations. [8 marks]
(ii) What is the temperature of the coke after 20 minutes?
[2 marks]

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ORDINARY DIFFERENTIAL EQUATIONS WITH APPLICATIONS
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(2) Consider the following second-order differential equation

2
2
dx
yd
dy
x





1



2/32
2
xxyx
dx
x cos
4
(i) Given that one of the solution is
y
sin
1

x
x

. Find the other
solution using method of reducing the order and thus write
down the complementary solution (
y
). [10 marks]

(ii) Find the Wronskian
),(
yyW
of the two solutions (i) and
decide whether they are linearly independent or dependent.
11
c
[2 marks]

(iii) Find the particular solution (
y
) in its simplest form by
solving the non-homogeneous part of the equation using
p
method of variation of parameter. Then write down the
general solution. [8 marks]
(3) Use the method of undetermined coefficient to find the general
solution of the given differential equation.
)4(

cos520’4”5”’124 
x
x
[10 marks]

2
2
exeyyyyy