Question

The difference of the order and the degree of the differential equation \[ \Big( \frac{d^2 y}{dx^2} \Big)^2 + \Big( \frac{dy}{dx} \Big)^3 + x^4 = 0 \text{ is:} \]

• A. 1
• B. 2
• C. -1
• D. 0

Hint:

Order = highest derivative’s order. Degree = its power after making the equation polynomial in derivatives.

Answer 1

The Correct Option is A

- The order is the highest derivative present: here, $\frac{d^2 y}{dx^2}$. So, Order = 2.
- The degree is the power of the highest order derivative after making it free from radicals or fractions: here, $\Big( \frac{d^2 y}{dx^2} \Big)^2$, so Degree = 2.
- Difference = Order - Degree = 2 - 1 = 1.
Wait! There is a mistake here — the degree is the exponent of the highest order derivative: \[ \Big( \frac{d^2 y}{dx^2} \Big)^2 \implies \text{Degree} = 2. \] So, \[ \text{Difference} = 2 - 2 = 0. \] So, final answer: (D) 0.