Question

The order of the differential equation \( \left( \frac{d^3y}{dx^3} \right)^2 + \log x \left( \frac{d^2y}{dx^2} \right)^3 + 5y = \cos x \) will be

• A. 2
• B. 3
• C. 5
• D. 6

Hint:

To find the order of a differential equation, simply look for the derivative with the most "primes" or the highest number in the 'd' term (like \(d^n y\)). Don't be distracted by the powers (degree) or other terms like \(\log x\) or \(\cos x\). The order is determined solely by 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. The degree of a differential equation is the power of the highest order derivative, provided the equation is a polynomial in its derivatives. The question asks for the order.
Step 2: Detailed Explanation:
Let's examine the given differential equation: \[ \left( \frac{d^3y}{dx^3} \right)^2 + \log x \left( \frac{d^2y}{dx^2} \right)^3 + 5y = \cos x \] We need to identify the derivatives present in the equation.
The derivatives are \( \frac{d^3y}{dx^3} \) and \( \frac{d^2y}{dx^2} \).
The order of \( \frac{d^3y}{dx^3} \) is 3.
The order of \( \frac{d^2y}{dx^2} \) is 2.
The highest order among all the derivatives in the equation is 3.
Step 3: Final Answer:
The order of the highest derivative (\( \frac{d^3y}{dx^3} \)) is 3. Therefore, the order of the differential equation is 3.