Analysis and Approaches for IBDP Maths Ebook 2 | Page 221

Exercise 68
dy
xy
1. Consider the differential equation � , where 10
2
dx
x � 9
y � when x � 4 . Use Euler’s
method with a step length of 0.1 to find an approximation for the value of y when
x � 4.3 .
[6]
2. Consider the differential equation d y x
e 4y
dx � � , where y � 2 when x � 0 . Use Euler’s
method with a step length of 0.2 to find an approximation for the value of y when
x � 0.8 .
[7]
15
dy
y 1
3. Consider the differential equation � � , where y � 2 when x � 1. Use Euler’s
3
dx x x
method with a step length of 0.25 to find an approximation for the value of y when
x � 2 .
[7]
4. Consider the differential equation 1d y
y 1
x dx � � � , where y � 3 when x � 3 . Use Euler’s
method with a step length of 0.2 to find an approximation for the value of y when x � 4 .
[9]
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