Analysis and Approaches for IBDP Maths Ebook 2 | Page 214

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Chapter
15
Differential Equations
SUMMARY POINTs
�
dy
dx �
f ( x, y)
: First order differential equation
� Solving d y
� f ( x) g( y)
by separating variables:
dx dy
1
� f ( x) g( y) � d y f ( x)dx
d x
� �
g( y)
�
� Solving d y
� f ( x) � y � g( x, y)
by integrating factor:
dx e �
f ( x)dx
: Integrating factor
dy
f ( x)d x dy
f ( x)d x f ( x)dx
� f ( x) � y � g( x, y) � e� � e� � f ( x) � y � e�
� g( x, y)
dx
dx
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