Question

The degree of the differential equation \( (y'')^2 + (y')^3 = x \sin(y') \) is:

• A. \( 1 \)
• B. \( 2 \)
• C. \( 3 \)
• D. Not defined

Hint:

The degree of a differential equation cannot be defined if it includes any non-polynomial terms involving derivatives.

Answer 1

The Correct Option is D

Step 1: Definition of the degree of a differential equation.
The degree of a differential equation is determined only when the equation is a polynomial in all of its derivatives. Step 2: Examine the given equation.
The provided equation is: \[ (y'')^2 + (y')^3 = x \sin(y'). \] This equation includes a non-polynomial term, \( \sin(y') \), where \( y' \) is a derivative. Therefore, the degree of the equation cannot be defined. Step 3: Final Answer.
Thus, the degree of this differential equation is: \[ \boxed{\text{Not defined}}. \]