Question

The solution of \( \frac{d^2x}{dy^2} = k \), where \( k \) is a non-zero constant, vanishes when \( y = 0 \) and tends to finite limit as \( y \to \infty \), is

• A. \( x = k(e^y + e^{-y}) \)
• B. \( x = k(e^y + e^{-y} - 2) \)
• C. \( x = k(e^y - e^{-y}) \)
• D. \( x = k(e^y - 1) \)

Hint:

When solving second-order differential equations, find the general solution first and then apply boundary conditions to solve for the constants.

Answer 1

The Correct Option is A

The second-order differential equation is solved using the method for solving differential equations with constant coefficients.