The order and the degree of the differential equation \(\left(\displaystyle\frac{d^2y}{dx^2}\right)^{2/3} = 1 + \displaystyle\frac{dy}{dx}\) are
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → order 2, degree 2
The highest derivative present is \(\frac{d^2y}{dx^2}\), so
\(\text{order} = 2\)
A degree is always a positive whole number, so the fractional power must be removed first. Cubing both sides:
\( \displaystyle \left(\frac{d^2y}{dx^2}\right)^{2} = \left(1 + \frac{dy}{dx}\right)^{3} \)
Now the highest derivative \(\frac{d^2y}{dx^2}\) appears with power 2, so
\(\text{degree} = 2\)
The power 3 belongs to \(\frac{dy}{dx}\), which is not the highest derivative.