Question

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

• A. order 2, degree 2
• B. order 2, degree 1
• C. order 2, degree not defined
• D. order 1, degree not defined

Hint:

To determine the order of a differential equation, look for the highest derivative. The degree is the power of the highest derivative if it is an integer.

Answer 1

The Correct Option is C

The order of the differential equation is determined by the highest derivative of $y$ with respect to $x$. Here, the highest derivative is $\frac{d^2y}{dx^2}$, so the order is 2. The degree of the differential equation is not defined because the equation involves non-integer powers of derivatives. Thus, the degree is not defined.