Solve the Bernoulli equation using the appropriate substitution.

$y^{\text{'}}=y(x{y}^3-1)$

Possible Answers

$(a.)y^{-3}=x+\frac{1}{3}+C{e}^{-3x}$

$(b.)y^{-3}=x+\frac{1}{3}+C{e}^{3x}$

$(c.)y^{-3}=x-\frac{1}{3}+C{e}^{-3x}$

$(d.)y^{-3}=x-\frac{1}{3}+C{e}^{3x}$

$(e.)$ None $of$ the above