Question Number 129034 by oustmuchiya@gmail.com last updated on 12/Jan/21
$${Differentiate}\:\boldsymbol{{siny}}\:−\boldsymbol{{x}}^{\mathrm{2}} \boldsymbol{{y}}^{\mathrm{3}} −\boldsymbol{{cosx}}=\mathrm{3}\boldsymbol{{y}} \\ $$
Answered by MJS_new last updated on 12/Jan/21
$$\left(\mathrm{cos}\:{y}\:−\mathrm{3}{x}^{\mathrm{2}} {y}^{\mathrm{2}} \right){dy}+\left(−\mathrm{2}{xy}^{\mathrm{3}} +\mathrm{sin}\:{x}\right){dx}=\mathrm{3}{dy} \\ $$$$\Rightarrow \\ $$$$\frac{{dy}}{{dx}}=\frac{\mathrm{sin}\:{x}\:−\mathrm{2}{xy}^{\mathrm{3}} }{\mathrm{3}{x}^{\mathrm{2}} {y}^{\mathrm{2}} +\mathrm{3}−\mathrm{cos}\:{y}} \\ $$