Solving second order differential equation with mixed partials

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Suppose I wish to solve a differential equation of second order for $y(x)$ with form $$Ay''(x)+Bxy'(x)+Cy(x)=0$$ We are able to solve using substitution for a guessed exponential form if the $Bxy'(x)$ were a $By'(x)$. How do we deal with the fact that the variable of differentiation is there to solve?