Question

The order and degree of the differential equation \[ 3x^2 \frac{d^2 y}{dx^2} - \sin\left( \frac{d^3 y}{dx^3} \right) + \cos(xy) = 0 \] are:

• A. Order can't be defined and degree is 3
• B. Order is 3 and degree can't be defined
• C. Order is 3 and degree is 1
• D. Order is 1 and degree is 3

Hint:

Degree is defined only when the equation is polynomial in its highest order derivative.

Answer 1

The Correct Option is B

The highest derivative present is \( \frac{d^3 y}{dx^3} \), so the order is 3.
However, this derivative appears inside a non-polynomial function \( \sin \left( \cdot \right) \), so degree is not defined (as degree requires the differential equation to be polynomial in derivatives).