The degree of the differential equation \(\displaystyle\left(2+\left(\frac{dy}{dx}\right)^2\right)^{\frac{3}{2}}=a^2\frac{d^2y}{dx^2}\) is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 2
The degree is the power of the highest order derivative once the equation is a polynomial in the derivatives. The left side has the fractional power \(\frac{3}{2}\), so both sides are squared:
\( \displaystyle \left(2+\left(\frac{dy}{dx}\right)^2\right)^{3} = a^4\left(\frac{d^2y}{dx^2}\right)^2 \)
The highest order derivative is \(\frac{d^2y}{dx^2}\), and it now appears with power 2. So the degree is 2.
Tip: Read the degree only after the fractional powers are removed. In the printed form \(\frac{d^2y}{dx^2}\) has power 1, which is a common wrong answer.