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Question

If the curve satisfying yy1sinx=cosx(sinxy2) passes through (π2,2), then the value of 3(y(π6))2 is equal to

A
81
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B
61
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C
41
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D
21
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Solution

The correct option is C 41
Given differential equation,
dydxy=cotx(sinxy2)
Take y2=t2ydy=dt
dt2dx=cotx(sinxt)
dtdx+2tcotx=2cosx
Integrating Factor,I=e2cotxdx=e2ln(sinx)
te2ln(sinx)=2cosxe2ln(sinx)dx
te2ln(sinx)=2sin3x3+C
y2sin2x=2sin3x3+C
Given y(π/2)=2C=103
3(y(π/6))2=41

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