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Basic Mathematics-II
Notes Integrating, we get
1 v
log x v 2v 1 dv
1 1
v 2v dv
1
1
log v log 2v 1 logc 1
2
or 2log x 2log v log 2v 1 log ,c 2log c 1 log c
2 2
x v
or log lgc
2v 1
2 2
x v
or c
2v 1
y 2
2
x 2
x c y
v
or x
y
2 1
x
xy 2
or
2y x
or xy 2 c 2y x
which is the required general solution.
2
Example: Solve xdy y dx x 2 y dx .
Solution:
dy y x 2 y 2
Here ….(1)
dx x
dy y x 2 y 2
Putting y = vx, so that
dx x
(1) reduces to
dv 2
v x 1 v
v
dx
dv 2
or x 1 v
dx
dv dx
or 2 .
1 v Dx
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