Question

${e}^{x} \sin(y) dx + {e}^{x} \cos(y) dy = y \sin(xy) dx + x \sin(xy) dy$
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Answer 1

Answer:

Your equation is nothing but a exact differential

$\frac{d}{dx} ( {e}^{x} \sin(y) ) = \frac{d}{dx} ( - \cos(xy) )$

Open the derivative you get the visual