Analysis and Approaches for IBDP Maths Ebook 2 | Page 218

Your Practice Set – Analysis and Approaches for IBDP Mathematics
67
Paper 2 Section A – Integrating Factor
Example
Solve the differential equation
answer in the form y � f ( x)
.
x
8x
dy
e
�4x y � , where
dx
x
3 2
8
e
y � when x � 1, giving the
8
[9]
Solution
x
dy
e
�4x y �
dx
x
3 2
8x
8x
dy
4 e
� y � (A1) for correct approach
4
dx x x
The integrating factor
4 dx
x
� e �
(M1) for valid approach
4ln x
� e
4
ln x
� e
4
� x
A1
dy
4 e
dx x x
4 dy
3 8x
x 4x y e
dx d ( 4 8x
yx � e
dx
(A1) for correct approach
4
yx � � e 8x
dx
8x
4 4 4
�x � x � y � x �
4
(M1) for valid approach
1
8
4 8x
yx � e � C
yx
4
e
�
8x
� C
8
8x
e � C
y � A1
4
8x
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