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
Answer & explanation
Correct answer: option 3
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 = $1 + 4 = 5$