$\frac{dy}{dx}=xy,\:y\left(0\right)=1$

$\left(4-8x\right)^{-\frac{1}{2}}$

$\frac{dy}{dx}-\frac{3y}{x}=7$

$\ln\sqrt{\frac{x^2}{y^3}}$

$y'\cdot y+x=0$

$\lim_{x\to0}\left(\frac{log\left(x^2+ax+1\right)-\frac{x^2}{2}-ax}{x^2}\right)$

$\int_0^{\infty}\left(\frac{3}{x^5-16x}\right)dx$