$\sin\left(\frac{y}{x}\right)dy=\frac{y\sin\left(\frac{y}{x}\right)+x}{x}dx$

$\frac{d}{dx}6x^3\sqrt{y}+6y=18$

$\frac{3x+5}{3}-\frac{1}{2}>\frac{1}{6}$

$\frac{x^2+15x+51}{x+8}$

$xy+\left(1+x^2\right)\frac{dy}{dx}=2x\left(1+x^2\right)^3$

$-y^{3}+4+y^{3}+7x^{2}+3-5y^{3}+3$

$\frac{dy}{dx}=xy-x-2y-2$