The initial populations of horse and zebra are 7000 and 2000 respectively .
( e ) Find the particular solution of
( i ) x ;
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( ii ) y .
( f ) Hence , state the long-term behaviour for the population of horse .
( g ) On the following diagram , sketch the following trajectory for this particular solution .
[ 5 ]
[ 1 ]
[ 2 ]
3 . A particle moves in a straight line with velocity v ms
� 1 and displacement m
x with respect to the starting point O . By considering the rate of change of its velocity , the relationship between the variables can be modelled by the differential equation
2 d x dx � 3 � 4x � 0 .
2 dt dt
dx
( a ) By using v � , express the differential equation in a coupled system . dt
[ 1 ] Euler ’ s method with a step length of 0.1 is used to approximate the displacement of the
1 particle at t � 0.3 . It is given that initially the particle is at O with velocity 1 ms � .
( b ) Find , when t � 0.1, the approximate value of
( i ) v ;
( ii ) x . [ 4 ] www . seprodstore . com
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