Question

The order and degree of the differential equation \[ \left[ \left( \frac{d^2 y}{dx^2} \right)^2 - 1 \right]^2 = \frac{dy}{dx} \text{ are, respectively:} \]

• A. 2, 2
• B. 2, not defined
• C. 1, 2
• D. 2, not defined

Hint:

To find degree, first make sure the equation is polynomial in derivatives. The highest exponent of the highest order derivative (after simplification) gives the degree.

Answer 1

The Correct Option is A

To find the order and degree:
- The order is the highest derivative present in the equation. Here, the highest derivative is $\frac{d^2 y}{dx^2}$, so the order is 2. 
- The degree is the power of the highest order derivative after removing all fractional powers and roots. The term $\left( \frac{d^2 y}{dx^2} \right)^2$ appears inside a square again, making it of power 2 × 2 = 4 originally. 
But we observe it appears as $\left[ \left( \frac{d^2 y}{dx^2} \right)^2 - 1 \right]^2$. 
So the degree with respect to the highest derivative (i.e., $d^2y/dx^2$) is 2.