(1) A cold beer with an initial temperature of
warms up to
10 minutes while sitting in a room of temperature
(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) Consider the following second-order differential equation
(i) Given that one of the solution is
. Find the other
solution using method of reducing the order and thus write
down the complementary solution (
). [10 marks]
(ii) Find the Wronskian
of the two solutions (i) and
decide whether they are linearly independent or dependent.
(iii) Find the particular solution (
) in its simplest form by
solving the non-homogeneous part of the equation using
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.