Analysis and Approaches for IBDP Maths Ebook 2 | Page 223

Exercise 69
1. Consider the differential equation
dy
d
4y
e
2x
x � � , where 1
Maclaurin series for y up and including the term in
2
x .
y � when x � 0 . Find the
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2. Consider the differential equation d y
xy ln( x 1)
dx � � � , where x �� 1.
y �� 2 when x � 0 .
Find the Maclaurin series for y up and including the term in
3. Consider the differential equation
e
2x
d
Maclaurin series for y up and including the term in
2
x .
y x
e y 1
dx � � , where y� e when x � 0 . Find the
2
x .
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4. Consider the differential equation
3x dy
2 3x �3x
e � (3x � 2x �1) e y � e � 0, where y � 2
dx
when x � 0 . Find the Maclaurin series for y up and including the term in
3
x .
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