( c )
1 ( 0 )
2 ln ( 32 0
5 ) � � � C
( M1 ) for substitution
2 0 � ln 32 � C C �� ln32
( A1 ) for correct value � 1 2 5 ln ( 32 ) ln 32 2 y � � x � y
� 2ln ( 32 � x ) � 2ln 32
2 5
12 y
5
� 2ln ( 32 � x ) � 2ln 32 A1
[ 3 ]
Exercise 54
1 . Consider the differential equation dx dt
2
� , where t , 0
� xsin�t x � .
( a ) Express
1
� dx as an indefinite integral of t . x
( b ) Hence , using the substitution u� �t to find the expression of ln x , giving the answer in terms of t .
It is given that x � 1 when t � 0.5 .
( c ) Find the expression of x .
[ 2 ]
[ 3 ]
[ 3 ]
2 . Consider the differential equation d y y
� dx
2x� 3 , where x , y � 0.
( a ) Express
1
� dx as an indefinite integral of x . y
[ 2 ]
( b ) Hence , using the substitution u�2x� 3 to find the expression of ln y , giving the answer in terms of x .
It is given that y � 12 when x � 3.
[ 3 ]
( c ) Find the expression of y . [ 3 ] www . seprodstore . com
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