Question

Assertion (A) The degree of the differential equation $\frac{d^{2}y}{d{x}^2}+3{\left(\frac{dy}{dx}\right)}^2=x^2\log \left(\frac{d^{2}y}{d{x}^2}\right)$ is not defined.
Reason (R) If the differential equation is a polynomial in terms of its derivatives, then its degree is defined.

• A. Both A and R are correct; R is the correct explanation of A
• B. Both A and R are correct; R is not the correct explanation of A
• C. A is correct; R is incorrect
• D. R is correct; A is incorrect

Answer 1

Answer: (A)

The given differential equation is
$\frac{d^{2}y}{d{x}^2}+3{\left(\frac{dy}{dx}\right)}^2=x^2\log \left(\frac{d^{2}y}{d{x}^2}\right)$
This is not a polynomial equation in terms of its derivatives.
$\therefore$ Its degree is not defined.