dy y 1 3 . Consider the differential equation � � , where y � 2 when x � 1. Euler ’ s method
3 dx x x with a step length of 0.25 is used to approximate the value of y when x � 2 .
( a ) Find the approximate value of y when x � 1.25 .
( b ) Hence , write down the approximate value of y when
[ 3 ]
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( i ) x � 1.5;
( ii ) x � 1.75 , giving the answer correct to 4 decimal places ;
( iii ) x � 2 . [ 3 ]
4 . Consider the differential equation d y x xy 0 dx � � � , where y � 3 when x � 3. Euler ’ s method with a step length of 0.2 is used to approximate the value of y when x � 4 .
( a ) Find the approximate value of y when x � 3.2 .
( b ) Hence , write down the approximate value of y when
[ 3 ]
( i ) x � 3.4 ;
( ii ) x � 3.6 , giving the answer correct to 4 decimal places ;
( ii ) x � 3.8, giving the answer correct to 4 decimal places ;
( iii ) x � 4 . [ 4 ] www . seprodstore . com
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