Determine whether the given differential equation is separable.

StartFraction dy Over dx EndFraction equals $4$ y squared minus $8$ y plus $6$dydx$=4$y$28$y$+6$

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Part $1$

Is the differential equation$$ separable?

A$.$

$$Yes; because

StartFraction dy Over dx EndFraction equals g left parenthesis x right parenthesis p left parenthesis y right parenthesisdydx$=$g$($x$)$p$($y$)$

where

$$g$($x$)$equals$=1$

and

$$p$($y$)$equals$=4$ y squared minus $8$ y plus $64$y$28$y$+6.$

B$.$

$$Yes; because

StartFraction dy Over dx EndFraction equals g left parenthesis x right parenthesis p left parenthesis y right parenthesisdydx$=$g$($x$)$p$($y$)$

where

$$g$($x$)$equals$=66$

and

$$p$($y$)$equals$=4$ y squared minus $8$ y$4$y$28$y$.$

C$.$

$$Yes; because

StartFraction dy Over dx EndFraction equals g left parenthesis x right parenthesis p left parenthesis y right parenthesisdydx$=$g$($x$)$p$($y$)$

where

$$g$($x$)$equals$=44$

and

$$p$($y$)$equals$=$y squared minus $4$ y plus $3$y$24$y$+3.$

D$.$

No