The sum of the order and degree of the differential equation representing the family of curves $y = mx + m^4$, where $m$ is arbitrary constant, is

5

The correct answer is Option (3) → 5 **

Given family: $y = mx + m^{4}$

Differentiate w.r.t. $x$:

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

So $m = \frac{dy}{dx}$

Substitute into original:

$y = x\frac{dy}{dx} + \left(\frac{dy}{dx}\right)^{4}$

Rearrange:

$y - x\frac{dy}{dx} - \left(\frac{dy}{dx}\right)^{4} = 0$

Highest derivative: $\frac{dy}{dx}$ → order = 1

Highest power: $4$ → degree = 4

Sum = $1 + 4 = 5$