The sum of order and degree of differential equation
\(2x^2 \cdot \left(\displaystyle\frac{d^2y}{dx^2}\right) - 3 \cdot \left(\displaystyle\frac{dy}{dx}\right)^3 + y = 0\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 3
The highest order derivative in the equation is \(\frac{d^2y}{dx^2}\), so the order is 2.
The equation is a polynomial in the derivatives, and the highest order derivative \(\frac{d^2y}{dx^2}\) appears with power 1, so the degree is 1.
\(\text{Order} + \text{Degree} = 2 + 1 = 3\)
Tip: The degree is the power of the highest order derivative, not the largest power seen in the equation. The cube on \(\frac{dy}{dx}\) does not count, so taking the degree as 3 (sum 5) is wrong.