Siny dy/dx= cosy(1-xcosy)

pls i need it fast​

Correct option is
D
secye
−x
=e
−x
(x+1)+c.
siny
dx
dy
​
=cosy(1−xcosy)
⇒secytany
dx
dy
​
−secy=−x
Put secy=v⇒secytanydy=dx
∴
dx
dv
​
−v.1=−x ...(1)
Here P=−1⇒−∫dx=−x
∴I.F.=e
−x

Multiplying (1) by I.F. we get
e
−x

dx
dv
​
−e
−x
v=−xe
−x

Integrating both sides we get
e
−x
v=−∫xe
−x
dx+c=e
−x
(x+1)+c
⇒secye
−x
=e
−x
(x+1)+

Hope it helps you!!!

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