Your Practice Set – Applications and Interpretation for IBDP Mathematics
57
Paper 1 – More about Euler ’ s Method
Example
�dx
�( x � y) sin t
� dt
Consider the coupled differential equations �� . x � 3 and y � 4 when dy
�( x � y) cost
�� dt t � 0. Euler ’ s method with a step length of 0.1 is used to approximate the values of x and y when t � 0.2 .
( a ) Find , when t � 0.1, the approximate value of
( i ) x ;
( ii ) y .
( b ) Hence , write down , when t � 0.2 , the approximate value of
[ 4 ]
( i ) x ;
( ii ) y . [ 2 ]
Solution
( a ) ( i )
� � x �� y n�1
� x dx
�0.1 d t
dy
�0.1 d t
� n�1 n
�� tn� 1
�tn
�
� � � n
� y
( t , x , y )
( t , x , y )
0.1
n n n
n n n
( M1 ) for valid approach t0 � 0, x0 � 3, y0 � 4 ( A1 ) for correct values t1 � 0 � 0.1 � 0.1
�
� x1 � 3� 0.1 ( 3� 4 ) sin 0 � 3 A1
( ii ) y1 � 4 � 0.1 �( 3� 4 ) cos 0�
� 4.7 A1
[ 4 ]
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