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Question

Solution of the differential equation 2y sin xdydx=2 sin x cos xy2 cos x satisfying y(π2)=1)is given by


A
y2=sin x
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B
y=sin2 x
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C
y2=cos x+1
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D
y2=sin x=4cos2x
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Solution

The correct option is A y2=sin x
The given equation can be written as 2y sin xdydx+y2 cos x=sin 2x
ddx(y2 sin x)=sin 2xy2 sin x=(12)cos 2x+C.
So (y(π2))2 sin(π2)=(12)cos(2π2)+CC=12
Hence y2sinx=(12)(1cos2x)=sin2xy2=sinx

Mathematics

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