Analysis and Approaches for IBDP Maths Ebook 2 | Page 219

8 8(1)
e e � C
� (M1) for substitution
4
8 8(1)
8 8
e �e � C
C � 0
(A1) for correct value
8x
e
�y
�
4
8x
A1
[9]
Exercise 67
dy
y 1
1. Solve the differential equation � � , where
6
dx x x
in the form y � f ( x)
.
11
y � when x � 1, giving the answer
6
[8]
15
2. Solve the differential equation
answer in the form y � f ( x)
.
dy
x y x
d
2 x
2
x � � , where 3
y � when x � 1, giving the
ln 2
[9]
dy
3. Solve the differential equation
d
the answer in the form y � f ( x)
.
cos
x 2y tan x
3
x � � , where 3
y � when x � 0 , giving
[9]
dy
2
4. Consider the differential equation sin x cos x 1 y cos x
dx � � � , where y � � when
�
2x�sin 2x�3�
x � . Show that y � .
2
4sin x
[10]
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