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If $\frac{d y}{d x} = \frac{x y + y}{x y + x}$ , then the solution of the differential equation is

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y=xex+c

y=ex+c

y=Axex−y

y=x+A

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detailed solution

Correct option is C

∵dydx=y(x+1)x(y+1)⇒∫y+1ydy=∫x+1xdx ⇒∫dy+∫1ydy=∫dx+∫1xdx⇒y+ln⁡y=x+ln⁡x+c⇒ln⁡yx=x−y+c⇒yx=ex−y+c⇒y=xex−yec⇒y=Axex−y

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If dydx=xy+yxy+x, then the solution of the differential equation is

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If $\frac{d y}{d x} = \frac{x y + y}{x y + x}$ , then the solution of the differential equation is