Solution of the differential equation $(3 x y^{2} + x sin x y) d y + (y^{3} + y sin x y) d x = 0$ is:

x y^{3} - cos x y = c

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x y^{3} + cos x y = c

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x y^{2} - cos x y = c

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x y^{2} + cos x y = c

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Solution

The correct option is D $x y^{3} - cos x y = c$
${3 x y}^{2} d y + y^{3} d x + sin (x y) (x d y + y d x) = 0$ or $d ({x y}^{3}) + sin (x y) d (x y) = 0$
On integrating, we get
${x y}^{3} - cos x y = c$

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