$x=v y$ converts those differential equation to variable separable form which we have Homogenous function $f(x, y)=\frac{d y}{d x}$ of order zero ie each term should have equal power.
$\therefore$ Option (a) \& (b) are not homogeneous. Hence they are incorrect option. Option (c) have homogeneus function of order 1 because $\frac{d y}{d x}=\frac{y^2}{x+\sqrt{x y}}=f(x, y)$. Hence option (c) is also not correct.
Option (d) is correct because it have homogenous function of order zero $\frac{d y}{d n}=f(x, y)=\frac{-\left(1+2 e^{\frac{x}{y}}\right)}{2 e^{\frac{x}{y}}\left(1-\frac{x}{y}\right)}$