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 determined by the highest derivative present. The degree is the exponent of this highest derivative, provided all fractional powers have been eliminated. For the 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 \( \frac{d^2y}{dx^2} \), establishing the order as 2. - The degree of the highest derivative, \( \frac{d^2y}{dx^2} \), is 1, as it has an implicit exponent of one. Therefore, the sum of the order and degree is \( 2 + 1 = 3 \).