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$If x \cdot \ln x \cdot \frac{d y}{d x} + y = 2 \ln x, y (e) = 2 then y (e^{2}) =$

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Correct option is D

dydx+yx⋅ln⁡x=2x I.F =exp⁡∫dxx⋅ln⁡x=ln⁡x∴ soln is y⋅ln⁡x=2∫ln⁡xxdxy lnx=(lnx)2+cy=lnx+1lnxy(e2)=2+12=52

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If x⋅ln⁡x⋅dydx+y=2lnx, y(e)=2 then ye2=

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$If x \cdot \ln x \cdot \frac{d y}{d x} + y = 2 \ln x, y (e) = 2 then y (e^{2}) =$