Question

The order of the differential equation \( \left( \frac{d^3 y}{dx^3} \right)^2 + x \left( \frac{dy}{dx} \right)^3 + 8y = \log x \) is:

• A. 2
• B. 3
• C. 5
• D. 6

Hint:

The order of a differential equation is determined by the highest derivative of the dependent variable in the equation.

Answer 1

The Correct Option is B

Step 1: Identify the highest derivative term in the equation.

Step 2: The equation contains the third derivative \( \frac{d^3y}{dx^3} \) and the first derivative \( \frac{dy}{dx} \).

Step 3: Conclusion Since the highest order derivative is \( \frac{d^3y}{dx^3} \), the order of the differential equation is determined by this term.

The order of the differential equation is 3.

Thus, the correct answer is (B) 3.