Question

The order of the differential equation $2x^2 \frac{d^2 y}{dx^2} - 3 \frac{dy}{dx} + y = 0$ will be:

• A. $0$
• B. $1$
• C. $2$
• D. None of these

Hint:

The order of a differential equation is determined by the highest derivative of the dependent variable with respect to the independent variable.

Answer 1

The Correct Option is C

Step 1: Definition of order of a differential equation.
The order of a differential equation is defined as the highest power of the derivative that appears in the equation.

Step 2: Analyze the given equation.
The given differential equation is: \[ 2x^2 \frac{d^2 y}{dx^2} - 3 \frac{dy}{dx} + y = 0. \] Here, the highest derivative is $\frac{d^2 y}{dx^2}$, which is the second derivative.

Step 3: Conclusion.
Since the highest derivative is the second derivative, the order of the differential equation is 2.

Final Answer: The correct answer is (C) $2$.