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A solution of the differential equation $y x^{y - 1} d x + x^{y} \ln x d y = 0$ , when $y (2) = 1$ is

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yx=1

xy+1=0

1y=log2x

x=log2y

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detailed solution

Correct option is C

yxy−1+xylog⁡xdy=0⇒dxy=0⇒∫dxy=∫0dx⇒xy=cy(2)=1⇒c=2xy=2⇒yln⁡x=ln⁡2 ⇒1y=log2⁡x

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A solution of the differential equation yxy−1dx+xylnxdy=0, when y2=1 is

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A solution of the differential equation $y x^{y - 1} d x + x^{y} \ln x d y = 0$ , when $y (2) = 1$ is