Question

The order of the differential equation \[ \left(\frac{d^5y}{dx^5}\right)^2 + \frac{dy}{dx} + y^2 = 0 \] is: 

• A. 1
• B. Not defined
• C. 5
• D. 2

Hint:

Order is the derivative's power, while degree is the exponent of the highest derivative (provided the equation is a polynomial in derivatives).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The order of a differential equation is defined as the order of the highest derivative present in the equation.

Step 2: Detailed Explanation:
The derivatives present in the equation are \( \frac{d^5 y}{dx^5} \) (which is 5th order) and \( \frac{dy}{dx} \) (which is 1st order).
The highest derivative is 5. Therefore, the order is 5.

Step 3: Final Answer:
The order is 5.