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The solution of a[xdy + ydx] = xy dy

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x + y = xy + c

a log(xy) = y + c

x + c = a log(xy)

xy = y + c

answer is A.

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Detailed Solution

$\begin{array}{l} G i v e n a [x d y + y d x] = x y d y \\ \Rightarrow a \frac{D (x y)}{x y} = d y \\ \Rightarrow a \int \frac{D (x y)}{x y} = \int d y \\ \Rightarrow a \log (x y) = y + c \end{array}$

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