The general solution of the differential equation $$dydx+sinx+y2=sinx$$−$$y2$$ is

Correct option is 2logtany4=c−2sinx2

Questions

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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logtany2=c−2sinx

logtany4=c−2sinx2

logtany2+π4=c−2sinx

logtany2+π4=c−2sinx2

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detailed solution

Correct option is B

dydx=sin⁡x−y2−sin⁡x+y2 sinA-B-sinA+B=-2cosAsinB=−2cos⁡x2sin⁡y2⇒∫cos⁡ecy2⋅dy=−2∫cos⁡x2⋅dx⇒ln⁡tan⁡y412=−2⋅sin⁡(x2)12+2c⇒ln⁡|tan⁡(y4)|=c−2sin⁡x2

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The general solution of the differential equation dydx+sinx+y2=sinx−y2 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