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The solution of the differential equation $(\sin x + \cos x) d y + (\cos x - \sin x) d x = 0$ is

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exsinx+cosx+c=0

eysinx+cosx=c

excosx−sinx=c

eysinx−cosx=c

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detailed solution

Correct option is B

(sin⁡x+cos⁡x)dy+(cos⁡x−sin⁡x)dx=0∫dy=∫sin⁡x−cos⁡xsin⁡x+cos⁡xdx Put cos⁡x+sin⁡x=t⇒y=−∫dtt=−ln⁡t+ln⁡c⇒y=ln⁡csin⁡x+cos⁡x⇒ey=csin⁡x+cos⁡x⇒ey(sin⁡x+cos⁡x)=c

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The solution of the differential equation sinx+cosxdy+cosx−sinxdx=0 is

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The solution of the differential equation $(\sin x + \cos x) d y + (\cos x - \sin x) d x = 0$ is