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$The equation of the curve whose slope is \frac{y - 1}{x^{2} + x} and which passes through the point (1,0) is$

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xy+x+y-1=0

xy-x-y-1=0

y-1x+1=2x

yx+1-x+1=0

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detailed solution

Correct option is C

∫1x2+xdx=∫dyy−1⇒∫1x(x+1)dx=∫dyy−1⇒log⁡x−log⁡(x+1)=log⁡(y−1)+log⁡c⇒xx+1=c(y−1) pass (1,0)⇒c=-1/2⇒xx+1=−1/2(y−1)⇒xy+x+y−1=0

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The equation of the curve whose slope is y−1x2+x and which passes through the point (1,0) is

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$The equation of the curve whose slope is \frac{y - 1}{x^{2} + x} and which passes through the point (1,0) is$