Question

The order of the differential equation \( \frac{d^3y}{dx^3} + \frac{d^2y}{dx^2} + y \cos x = 0 \) is :

• A. 2
• B. 3
• C. 0
• D. Not defined

Hint:

Do not confuse the 'order' with the 'degree' of a differential equation. The 'degree' is the highest power of the highest-order derivative, after the equation has been cleared of radicals and fractions in its derivatives. The 'order' is simply the highest derivative itself.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The order of a differential equation is defined as the order of the highest derivative that appears in the equation.
Step 2: Detailed Explanation or Calculation:
The given differential equation is:
\[ \frac{d^3y}{dx^3} + \frac{d^2y}{dx^2} + y \cos x = 0 \] Let's identify the derivatives present in the equation:
- \( \frac{d^3y}{dx^3} \) is the third derivative (order 3).
- \( \frac{d^2y}{dx^2} \) is the second derivative (order 2).
The highest order among all the derivatives in the equation is 3.
Step 3: Final Answer:
Therefore, the order of the differential equation is 3.