In the following differential equation $\frac{d^2y}{dx^2}+x(\frac{dy}{dx})^2=2x^2\log(\frac{d^2y}{dx^2})$ order and degree is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → order 2, degree not defined
Given differential equation: $\frac{d^2y}{dx^2} + x \left(\frac{dy}{dx}\right)^2 = 2x^2 \log\left(\frac{d^2y}{dx^2}\right)$
Step 1: Identify the highest order derivative: $\frac{d^2y}{dx^2}$ → Order = 2
Step 2: Check degree: The highest order derivative appears inside a logarithm → cannot be expressed as a polynomial in $\frac{d^2y}{dx^2}$
Hence, Degree = Not defined
Answer: Order = 2, Degree = Not defined