( b ) ( i ) x2 � 3.076871731 x2 � 3.08
A1
( ii ) y2 � 5.466153207 y2 � 5.47
A1 [ 2 ]
12
Exercise 57
�dx
� x � yt
� dt
1 . Consider the coupled differential equations �� . x � 5 and y � 2 when t � 1. dy
� xt � y
�� dt Euler ’ s method with a step length of 0.15 is used to approximate the values of x and y when t � 1.3 .
( a ) Find , when t � 1.15 , the approximate value of
( i ) x ;
( ii ) y .
( b ) Hence , write down , when t � 1.3 , the approximate value of
[ 4 ]
( i ) x ;
( ii ) y . [ 2 ]
�dx
�( 2 � yt )
� dt
2 . Consider the coupled differential equations �� . x � 1.1 and y � 1 when dy
�( 2 �xt )
�� dt t � 0.97 . Euler ’ s method with a step length of 0.01 is used to approximate the values of
x and y when t � 1.
( a ) Find , when t � 0.98 , the approximate value of
( i ) x ;
( ii ) y . [ 4 ] www . seprodstore . com
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