Question

Order of differential equation \( xy \frac{d^2y}{dx^2} + x \left( \frac{dy}{dx} \right)^2 - y \frac{dy}{dx} = 0 \) is 2.

Hint:

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

Answer 1

Step 1: Identifying the order of the differential equation.
The given equation is: \[ xy \frac{d^2y}{dx^2} + x \left( \frac{dy}{dx} \right)^2 - y \frac{dy}{dx} = 0. \] The highest derivative of \( y \) with respect to \( x \) in this equation is \( \frac{d^2y}{dx^2} \), which is the second derivative.

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