Write the degree of the differential equation $5x\left(\frac{dy}{dx}\right)^2-\frac{d^2y}{dx^2}-6y=\log x$.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1
The given differential equation is $5x\left(\frac{dy}{dx}\right)^2-\frac{d^2y}{dx^2}-6y=\log x$
The highest order derivative present in the given differential equation is $\frac{d^2y}{dx^2}$ and each term in the derivative is a polynomial, so its degree is the highest exponent of $\frac{d^2y}{dx^2}$, which is 1.
Thus, the degree of the given differential equation is 1.