Your Practice Set – Applications and Interpretation for IBDP Mathematics
( b ) Hence , write down , the approximate value of
( i ) x when t � 0.99 ;
( ii ) y when t � 0.99 ;
( iii ) x when t � 1;
( ii ) y when t � 1.
[ 4 ]
2 d x dx
3 . Consider the differential equation �8 �15x
� 0 . x � 0 and d x 1
2 dt dt dt � when t � 2. Euler ’ s method with a step length of 0.1 is used to approximate the value of x when t � 2.2.
( a ) By using dx u � , express the differential equation in a coupled system . dt
( b ) Find , when t � 2.1, the approximate value of
[ 1 ]
( i ) u ;
( ii ) x .
( c ) Hence , write down , when t � 2.2, the approximate value of x .
[ 4 ]
[ 1 ]
2 d x dx
4 . Consider the differential equation �12 � 36x � 0 . x � 2 and d x
3
2 dt dt dt � when t � 0. Euler ’ s method with a step length of 0.05 is used to approximate the value of x when t � 0.1.
( a ) By using dx u � , express the differential equation in a coupled system . dt
( b ) Find , when t � 0.05 , the approximate value of
[ 1 ]
( i ) u ;
( ii ) x .
( c ) Hence , write down , when t � 0.1, the approximate value of x .
[ 4 ]
[ 1 ]
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