Question

Write the order of the differential equation \[ \sqrt{1 + \left( \frac{dy}{dx} \right)^2} = \left( \frac{d^2y}{dx^2} \right)^{\frac{3}{2}}. \]

Hint:

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

Answer 1

Step 1: Identify the highest derivative.
The given equation involves the first derivative \( \frac{dy}{dx} \) and the second derivative \( \frac{d^2y}{dx^2} \). The highest derivative present is \( \frac{d^2y}{dx^2} \).

Step 2: Determine the order.
The order of a differential equation is determined by the highest order of the derivative of \( y \). In this case, the highest order is 2 because \( \frac{d^2y}{dx^2} \) is the highest derivative.

Final Answer: \[ \boxed{2} \]