Analysis and Approaches for IBDP Maths Ebook 2 | Page 217

Exercise 66
1. Consider the differential equation
dx
dt
2
� , where 1
� xsin�t
x � when t � 0.5 .
(a) Express x in terms of t .
(b) Write down the range of values of x .
[8]
[2]
dy
B
2. Consider the differential equation � , where B is a constant. y � 3 when x � 4 ,
2
dx
y
and y � 9 when x � 121. Find y when
61
x � .
3
[8]
15
3. Solve the differential equation
answer in the form y � f ( x)
.
dy
dx 3 2
�� y sin x, where 2
y � when x � 0 , giving the
[8]
4. Solve the differential equation d y y
�
, where
d x (2x � 3)ln y
answer in the form y � f ( x)
.
y
ln5
� when 1
e
x � , giving the
[9]
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207