Eliminate the arbitrary constant from $y^2 = 4ax$ to form the DE:

Differentiate: $2y\,dy/dx = 4a$ ⇒ $a = (y/2)(dy/dx)$. Sub back into $y^2 = 4ax$: $y^2 = 4 \cdot (y/2)(dy/dx) \cdot x = 2xy(dy/dx)$. Equivalent to $y^2 = x(dy/dx) \cdot $… hmm — actually $y^2 = 2xy\,dy/dx$, or $y = 2x\,dy/dx$. Cleanest: $y = 2x \cdot dy/dx$, i.e., $y\,dx = 2x\,dy$, equivalent to option B reading.