Question

For the differential equation \(\frac{d^3y}{dx^3}+cos(\frac{d^2y}{dx^2}) = 0\), which of the following is true ?

• A. Order = 3, degree = 1
• B. Order = 3, degree = 2
• C. Order = 3, degree is not defined
• D. Order = 2, degree is not defined

Hint:

Degree is defined only if the equation is a polynomial in the derivatives.

Answer 1

The Correct Option is C

Step 1: Test the polynomial condition
A differential equation has a degree only when it can be written as a polynomial in $y', y'', y''',\ldots$. A trigonometric function of a derivative breaks that.

Step 2: Conclude
Order 3, degree not defined. Option (C).

Final Answer:
Order 3, degree not defined. \[ \boxed{\text{(C)}\ \text{Order}=3,\ \text{degree not defined}} \]