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Question

Find the equation of the curve passing through the point (0,π3) and satisfying the differential equation sinxcosy dx+cosxsiny dy=0, wherex,y(0,π2)

A
secxy=2
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B
secxy=2
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C
secxsecy=2
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D
secyx=2
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Solution

The correct option is C secxsecy=2
Given differential equation
sinxcosy dx+cosxsiny dy=0
tanx dx=tany dy
Integrating both sides, we get
logsecx+logC=logsecy
secxsecy=C (1)
Equation (1) passes through (0,π3).
C=2
Therefore, equation of the curve is secxsecy=2

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