The family $Y = Ax + {A^3}$ of curves will correspond to a differential equation of order

Given family of curves is $y = Ax + {A^3}$

….(i)
$\Rightarrow$ $\frac{{dy}}{{dx}} = A$

Replacing $A$ by $\frac{{dy}}{{dx}}$ in Eq. (i),

we get
$y = x\frac{{dy}}{{dx}} + {\left( {\frac{{dy}}{{dx}}} \right)^3}$

$\therefore$ Order $= 1$