Question

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

• A. 2
• B. 3
• C. 5
• D. 6

Hint:

The order of a differential equation is the highest power of the highest derivative in the equation.

Answer 1

The Correct Option is B

Step 1: The order of a differential equation is determined by the highest derivative present.

Step 2: In the given equation, the highest derivative is \( \frac{d^3 y}{dx^3} \), which is the third derivative of \( y \). Thus, the order of the differential equation is 3.