The degree of the differential equation \(\displaystyle\frac{d^2y}{dx^2} = \left(1 + \displaystyle\frac{dy}{dx}\right)^{2/3}\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 3
The degree is read only when the equation is a polynomial in the derivatives. Here the right side has the fractional power \(\frac{2}{3}\), so it must be removed first.
Cubing both sides:
\( \displaystyle \left(\frac{d^2y}{dx^2}\right)^3 = \left(1 + \frac{dy}{dx}\right)^2 \)
The highest derivative is \(\frac{d^2y}{dx^2}\), and it now appears with power 3, so
\(\text{degree} = 3\)
Reading the degree as 1 from the original form is the usual slip: the power of \(\frac{d^2y}{dx^2}\) changes when the root is cleared.