Question

The sum of the order and degree of the differential equation \[ \left( 1 + \left( \frac{dy}{dx} \right)^2 \right) \frac{d^2y}{dx^2} = \left( \frac{dy}{dx} \right)^3 \] is:

• A. 2
• B. 5/2
• C. 3
• D. 4

Hint:

To find the sum of the order and degree, identify the highest derivative and its exponent in the equation.

Answer 1

The Correct Option is C

The order of a differential equation is the highest derivative present, and the degree is the exponent of the highest derivative (after making sure there are no fractional powers). In the given equation: \[ \left( 1 + \left( \frac{dy}{dx} \right)^2 \right) \frac{d^2y}{dx^2} = \left( \frac{dy}{dx} \right)^3, \] - The highest derivative is \( \frac{d^2y}{dx^2} \), so the order is 2. - The degree of the highest derivative \( \frac{d^2y}{dx^2} \) is 1, as it is not raised to any power. Thus, the sum of the order and degree is \( 2 + 1 = 3 \).