The family $y = Ax + A^3$ of curves is represented by differential equation of degree

3

The correct answer is Option (3) → 3 ##

$y = Ax + A^{3}$

$\frac{dy}{dx} = A$

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

$\left( \frac{dy}{dx} \right)^{3} + x \frac{dy}{dx} - y = 0$

• Highest order derivative = $\frac{dy}{dx} \rightarrow$ order = 1
• Highest power of of the highest order derivative $\frac{dy}{dx}$ = 3 $\rightarrow$ degree = 3