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Example
Paper 1 – Euler ’ s Method
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Consider the differential equation d y y
� , where y � 3 when x � 2 . Euler ’ s method dx 4x with a step length of 0.1 is used to approximate the value of y when x � 2.3 .
( a ) Find the approximate value of y when x � 2.1.
( b ) Hence , write down the approximate value of y when
[ 3 ]
( i ) x � 2.2 , giving the answer correct to 5 decimal places ;
( ii ) x � 2.3 . [ 2 ]
Solution
( a )
�x ��
� y
� x n�1
n�1
� x n
� y
0 0
n
�0.1 dy
�0.1 d x n n
( x , y )
( M1 ) for valid approach
�2 , y � 3 ( A1 ) for correct values x1 � 2 � 0.1 � 2.1
� 3 � y1
� 3� 0.1� �� 3.0375
�4 ( 2 ) �
( b ) ( i ) y2 � 3.073660714
A1 y2 � 3.07366 A1
[ 3 ]
( ii ) y3 � 3.108588677 y3 � 3.11
A1 [ 2 ] www . seprodstore . com
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