Question

A solution of the ODE \( \frac{d^2y}{dx^2} + \frac{dy}{dx} = 0 \) is such that \( y(0) = 2 \) and \( y'(0) = 3 \). The value of \( y''(0) \) is

• A. 4
• B. 2
• C. -3
• D. 0

Hint:

For solving higher order differential equations, differentiate the equation as needed and use initial conditions to find the required values.

Answer 1

The Correct Option is D

The given differential equation is \( \frac{d^2y}{dx^2} + \frac{dy}{dx} = 0 \). To solve for \( y \), we first need to integrate the equation and apply the initial conditions \( y(0) = 2 \) and \( y'(0) = 3 \). By differentiating and solving for the second derivative at \( x = 0 \), we find that \( y''(0) = 0 \).