Analysis and Approaches for IBDP Maths Ebook 2 | Page 222

Your Practice Set – Analysis and Approaches for IBDP Mathematics
69
Paper 2 Section A – Development of Maclaurin Series
Example
Consider the differential equation d y
(cos x) y sec x
dx � � , where y � 0 when x � 0 . Find
the Maclaurin series for y up and including the term in
2
x .
[5]
Solution
dy
(cos x)
y sec x
dx � �
dy
(cos x)
y sec x
dx � �
dy
� (cos 0)0 � sec 0 � 1
(A1) for correct value
x �
d x
0
2
d y
dy
� ( �sin x) y � cos x � sec x tan x
(A1) for correct approach
2
dx
dx
2
d y
2
dx
x�0
� ( �sin 0)(0) � (cos 0)(1) � sec 0 tan 0 � 1 (A1) for correct value
2 2
dy x d y
y � y(0)
� x � �
d x 2! d x
2
x�0 x�0
2
x
y� 0 � x(1) � (1) � M1
2
1 2
y � x � x � A1
2
[5]
212
SE Production Limited