The general solution of the differential equation $$dydx+$$$$sin$$⁡$$(x+y)2=$$$$sin$$⁡$$(x$$−$$y)2$$ is

Correct option is 2log tan(y/4)=C-2sin(x/2)

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$The general solution of the differential equation \frac{d y}{d x} + \sin \frac{(x + y)}{2} = \sin \frac{(x - y)}{2} is$

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logtan(y/2)=C-2sinx

log tan(y/4)=C-2sin(x/2)

logtany4+π4=C-2sin(x/2)

logtany2+π4=C-2sinx

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detailed solution

Correct option is B

dydx=sinx2-y2-sinx2+y2dydx=-2cosx2siny212dysiny2=-cosx2dx12∫cosecy2dy=-∫cosx2dx⇒ln tany4=−sinx212+C⇒ln tany4=C−2sinx2

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The general solution of the differential equation dydx+sin⁡(x+y)2=sin⁡(x−y)2 is

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$The general solution of the differential equation \frac{d y}{d x} + \sin \frac{(x + y)}{2} = \sin \frac{(x - y)}{2} is$