The solution of ( y ( 1 + x − 1 ) + s i n y ) d x + ( x + l o g x + x c o s y ) d y = 0 is Options: A . &nbsp ( 1 + y − 1 s i n y ) + x − 1 l o g x = C B . &nbsp ( y + s i n y ) + x y l o g x = C C . &nbsp x y + y l o g x + x s i n y = C D . &nbsp N o n e o f t h e s e

The solution of (y(1+x−1)+siny)dx+(x+logx+x cosy)dy=0 is

Question -

The solution of $(y (1 + x^{- 1}) + s i n y) d x + (x + l o g x + x c o s y) d y = 0$ is

Options:

A .

(1 + y^{- 1} s i n y) + x^{- 1} l o g x = C

B .

(y + s i n y) + x y l o g x = C

C .

x y + y l o g x + x s i n y = C

D .

N o n e o f t h e s e

Answer: Option C
:
C
The given equation can be written as

y (1 + x^{- 1}) d x + (x + l o g x) d y + s i n y d x + x c o s y d y = 0

\Rightarrow d (y (x + l o g x)) + d (x s i n y) = 0 \to y (x + l o g x) + x s i n y = C

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