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Question

Solve the differential equation: sinydydx=cosy(1xcosy)

A
secyex=ex(x+1)+c.
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B
secyex=ex(x1)+c.
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C
secyex=ex(x1)+c.
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D
secyex=ex(x+1)+c.
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Solution

The correct option is D secyex=ex(x+1)+c.
sinydydx=cosy(1xcosy)
secytanydydxsecy=x
Put secy=vsecytanydy=dx
dvdxv.1=x ...(1)
Here P=1dx=x
I.F.=ex
Multiplying (1) by I.F. we get
exdvdxexv=xex
Integrating both sides we get
exv=xexdx+c=ex(x+1)+c
secyex=ex(x+1)+c

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