18 . Let x and y be the number of soldiers , in thousands , from country X and country Y respectively . The changes in the number of soldiers in a battle between the two countries can be modelled by the coupled differential
equations
�dx
�( 13�2 yx ) � dt �
.
�dy �( 4x�16 ) y
�� dt
( a ) When y � 0, state the range of values of x such that d y
0 dt � . [ 1 ]
The initial numbers of soldiers from the two countries are both 4500 . Euler ’ s method with a step length of 0.05 is used to approximate the numbers of soldiers from the two countries when t � 0.05 .
( b ) Find the approximate numbers of soldiers from country Y at t � 0.05 . [ 4 ]
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