Question

Solve the differential equation: \[ \frac{d^2y}{dx^2} + 4y = 0 \]

• A. $y = C_1 \cos(2x) + C_2 \sin(2x)$
• B. $y = C_1 e^{2x} + C_2 e^{-2x}$
• C. $y = C_1 e^{x} + C_2 e^{-x}$
• D. $y = C_1 \cos(x) + C_2 \sin(x)$

Hint:

For second-order linear differential equations with constant coefficients, solve the characteristic equation to find the general solution.

Answer 1

The Correct Option is A

The characteristic equation is: \[ r^2 + 4 = 0 \] \[ r = \pm 2i \] Thus, the general solution is: \[ y = C_1 \cos(2x) + C_2 \sin(2x) \]