$y^2dx-x^3dy=0$
$x^2\frac{dy}{dx}-3\:x\:y=1$
$b^2+80b=0$
$125a^{12}-1000a^9b^{12}$
$\int\frac{x-8}{x^2+8}dx$
$\frac{\frac{y^4}{2}}{2y}$
$\int\frac{y^2}{\left(xy+1\right)^2}dy$
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