The degree of the differential equation \(\sqrt{1 + \left(\displaystyle\frac{dy}{dx}\right)^3} = 2\displaystyle\frac{d^2y}{dx^2}\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2
The degree is read only after the equation is made free of radicals in the derivatives.
Squaring both sides:
\( \displaystyle 1 + \left(\frac{dy}{dx}\right)^3 = 4\left(\frac{d^2y}{dx^2}\right)^2 \)
This is a polynomial in the derivatives. The highest derivative is \(\frac{d^2y}{dx^2}\) and its highest power is 2, so
\(\text{degree} = 2\)
The power 3 belongs to \(\frac{dy}{dx}\), which is not the highest derivative, so it does not decide the degree.