Question:
For the differential equation \(\frac{d^3y}{dx^3}+cos(\frac{d^2y}{dx^2}) = 0\), which of the following is true ?
For the differential equation \(\frac{d^3y}{dx^3}+cos(\frac{d^2y}{dx^2}) = 0\), which of the following is true ?
Show Hint
Degree is defined only if the equation is a polynomial in the derivatives.
Updated On: Oct 1, 2026
- Order = 3, degree = 1
- Order = 3, degree = 2
- Order = 3, degree is not defined
- Order = 2, degree is not defined
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The Correct Option is C
Solution and Explanation
Step 1: Order
The highest derivative is \(\frac{d^3y}{dx^3}\), so the order is \(3\).
Step 2: Degree
Degree is the power of the highest derivative once the equation is a polynomial in its derivatives. Here \(\cos\left(\frac{d^2y}{dx^2}\right)\) is not a polynomial in the derivative, so it cannot be cleared.
Step 3: Result
The degree is not defined. Option (C). Options (A) and (B) assign a degree, and option (D) gives the wrong order.
Final Answer:
Order is 3 and the degree is not defined. \[ \boxed{\text{(C)}\ \text{Order}=3,\ \text{degree not defined}} \]
The highest derivative is \(\frac{d^3y}{dx^3}\), so the order is \(3\).
Step 2: Degree
Degree is the power of the highest derivative once the equation is a polynomial in its derivatives. Here \(\cos\left(\frac{d^2y}{dx^2}\right)\) is not a polynomial in the derivative, so it cannot be cleared.
Step 3: Result
The degree is not defined. Option (C). Options (A) and (B) assign a degree, and option (D) gives the wrong order.
Final Answer:
Order is 3 and the degree is not defined. \[ \boxed{\text{(C)}\ \text{Order}=3,\ \text{degree not defined}} \]
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