Question

The Order of the differential equation $\left[ \frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^3 \right]^{6/5} = 6y$ is

• A. $3$
• B. $2$
• C. $6/5$
• D. $3$

Hint:

Order is the "rank" of the derivative (how many times you differentiated). Degree is the "power" of that specific highest-rank derivative after removing radicals. Order is usually much easier to spot!

Answer 1

The Correct Option is B

1. Defining the Order: The

Order of a differential equation is the order of the highest derivative present in the equation. It does not depend on whether the equation is in polynomial form or contains fractional powers.

2. Identifying Derivatives in the Equation: Looking at the given equation:

• Term 1: $\frac{d^2y}{dx^2}$ (This is a second-order derivative)

• Term 2: $\left(\frac{dy}{dx}\right)^3$ (This contains a first-order derivative)

3. Determining the Highest Order: The highest derivative appearing in the expression is the second derivative, $\frac{d^2y}{dx^2}$. Therefore, the order is 2.

Note on Degree: If the question asked for the

degree, we would first need to rationalize the equation by raising both sides to the power of $5$ to remove the fractional exponent $6/5$. The degree would then be the power of the highest order derivative. However, for

Order, this step is unnecessary.