Problem 02 | Elimination of Arbitrary Constants

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

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

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

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

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