A.
$\displaystyle xdy-ydx=\sqrt{x^{2}+y^{2}}dx$
B.
$\displaystyle \sqrt{y^{2}+1}dx=xydy$
how to solve these
$\displaystyle \sqrt{y^{2}+1}~dx=xy~dy$
$\displaystyle \frac{\sqrt{y^{2}+1}}{x}~dx=y~dy$
$\displaystyle \frac{dx}{x}=\frac{y}{\sqrt{y^{2}+1}}~dy$
$\displaystyle \int \frac{dx}{x}=\int \frac{y}{\sqrt{y^{2}+1}}~dy$
Use a substitution $\displaystyle u = y^{2}+1$ on the RHS.