Determine whether the following equations are second$-$order linear differential equations.

$($a$)y^{\text{'}\text{'}}=-4x(y{)}^2$

yes

no

$($b$)7\frac{d^{2}y}{d{x}^2}-8\frac{dy}{dx}+12y=0$

yes

no

$($c$)\frac{d^{2}y}{d{x}^2}=xsin(y)$

yes

no

$($d$)y^{\text{'}\text{'}}=3y{y}^{\text{'}}$

yes

no

$($e$)9y^{\text{'}\text{'}}-10y=6x^2+5x$

yes

no