Question

The degree of the differential equation \(\frac{d^2y}{dx^2} + 3 \left( \frac{dy}{dx} \right)^2 = x^2 \log \left( \frac{d^2y}{dx^2} \right)\) is

• A. \(1\)
• B. \(2\)
• C. \(3\)
• D. Not defined

Hint:

If any derivative appears inside functions like \(\log\), \(\sin\), \(e^x\), etc., then the degree is usually not defined.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The degree is the highest power of the highest order derivative when the equation is a polynomial in its derivatives.
Step 2: Key Formula or Approach:
If a derivative is inside a transcendental function like \(\log, \sin, e^x\), and cannot be freed, the degree is not defined.
Step 3: Detailed Explanation:
The term \(\log(d^2y/dx^2)\) involves the second-order derivative within a logarithm. This cannot be expressed as a polynomial.
Therefore, while the order is \(2\), the degree is not defined.
Step 4: Final Answer:
Degree is Not defined.