Taking the reciprocal on both sides, \begin{align} \frac{dx}{dy} &= 6e^{y} - 2x\newline \implies \diffone{x} + 2x &= 6e^{y}\newline \end{align} which is a linear differential equation. Considering the integrating factor as $exp \roundbr{\int 2dy} = exp \roundbr{2y}$, \begin{align} \implies \diffone{x}e^{2y} + 2xe^{2y} &= 6e^{3y}\newline \frac{d}{dy} \roundbr{xe^{2y}} &= 6e^{3y}\newline xe^{2y} &= \int 6e^{3y}dy + c = 2e^{3y} + c \end{align}

Another problem leveraging is the same transformation is \begin{align} \roundbr{y^{2} + 2x}\frac{dy}{dx} = y \end{align}