# Problem 02 | Elimination of Arbitrary Constants

**Problem 02**

$y \sin x - xy^2 = c$

**Solution 02**

$y \sin x - xy^2 = c$

$(y \cos x~dx + \sin x~dy) - (2xy~dy + y^2~dx) = 0$

$y \cos x~dx + \sin x~dy - 2xy~dy - y^2~dx = 0$

$(y \cos x~dx - y^2~dx) + (\sin x~dy - 2xy~dy) = 0$

$y(\cos x - y)~dx + (\sin x - 2xy)~dy = 0$ *answer*

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