Question

The solution of the differential equation $\frac{d^3 y}{dx^3} + \frac{d^2 y}{dx^2} + 4 \frac{dy}{dx} + 4y = 0$ is given by}

• A. $y = C_1 e^x + C_2 \cos 2x + C_3 \sin 2x$
• B. $y = C_1 e^{-x} + C_2 \cos 2x + C_3 \sin 2x$
• C. $y = C_1 e^{2x} + C_2 \cos 2x + C_3 \sin 2x$
• D. $y = C_1 e^{-2x} + C_2 \cos 2x + C_3 \sin 2x$

Hint:

Group terms immediately in polynomial auxiliary equations. Recognizing that $m = -1$ is a root allows factoring the cubic equation into a linear and a quadratic term without synthetic division.

Answer 1

The Correct Option is B