The order and degree of the differential function \[ \left[ 1 + \left( \frac{dy}{dx} \right)^2 \right]^5 = \frac{d^2y}{dx^2} \]

Question

Given that the solution of \[ \frac{d^2y}{dx^2} + \alpha \frac{dy}{dx} + \beta y = -e^{-x} \] is \[ y(x) = C_1 e^{-x} + C_2 e^{2x} + x e^{-x}, \] find the values of $\alpha$ and $\beta$.

Answer 1

The provided differential equation is: \[\left[ 1 + \left( \frac{dy}{dx} \right)^2 \right]^5 = \frac{d^2y}{dx^2}\] To determine the order and degree, we identify the highest order derivative and its power. * The highest derivative is $ \frac{d^2y}{dx^2} $, the second derivative. Thus, the order is 2. * The power of the highest derivative term $ \frac{d^2y}{dx^2} $ is 1. Therefore, the degree is 1. The order is 2 and the degree is 1.

The order and degree of the differential function \[ \left[ 1 + \left( \frac{dy}{dx} \right)^2 \right]^5 = \frac{d^2y}{dx^2} \]

Show Hint

The Correct Option is D

Solution and Explanation

Top Questions on Differential Equations

Questions Asked in CBSE Class XII exam