Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 56 dy xy 1 . Consider the differential equation � , where 10
2 dx x � 9 y � when x � 4 . Euler ’ s method with a step length of 0.1 is used to approximate the value of y when x � 4.3 .
( a ) Find the approximate value of y when x � 4.1.
( b ) Hence , write down the approximate value of y when
[ 3 ]
( i ) x � 4.2 , giving the answer correct to 5 decimal places ;
( ii ) x � 4.3 . [ 2 ]
2 . Consider the differential equation d y x e 4y dx � � , where y � 2 when x � 0 . Euler ’ s method with a step length of 0.2 is used to approximate the value of y when x � 0.8 .
( a ) Find the approximate value of y when x � 0.2 .
( b ) Hence , write down the approximate value of y when
[ 3 ]
( i ) x � 0.4 , giving the answer correct to 6 decimal places ;
( ii ) x � 0.6 , giving the answer correct to 6 decimal places ;
( iii ) x � 0.8 . [ 3 ]
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