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Division of a Polynomial by a Monomial

If 2xy - y2...

Question

If $(2 x y - y^{2} - y) d x = (2 x y + x - x^{2}) d y$ and y(1) =1, then the value of 12y (-1) is:

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Solution

The correct option is D 12
Given, $d (x^{2} y) = d (x y) + d (x y^{2})$
$\Rightarrow x^{2} y = x y + x y^{2} + c$
At $x = 1, y = 1$ $\Rightarrow$ c = -1
$\Rightarrow x^{2} y = x y + x y^{2} - 1 \Rightarrow y = - y + y^{2} - 1$
$∴ y^{2} + 2 y + 1 = 0 \Rightarrow y = - 1$
$∴ 12 y | y (- 1) | = 12$

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