?

Differential Equations

Free Version

Upgrade subject to access all content

Moderate

Inhomogeneous Equation with Trigonometric Forcing

DIFFEQ-VCQOCZ

Find out the general solution of $y''+2y'+5y=2e^{-x}\sin(2x)$.

A

$C_1e^{-x}\cos(2x)+C_2e^{-x}\sin(2x)+2e^{-x}\sin(2x)$

B

$e^{-x}(C_1\cos(2x)+C_2\sin(2x))-\frac{1}{2}xe^{-x}\cos(2x)$

C

$e^{-x}(C_1\cos(2x)+C_2\sin(2x))-\frac{1}{2}xe^{-x}\sin(2x)$

D

$e^{-x}(C_1\cos(2x)+C_2\sin(2x))-2e^{-x}\cos(2x)$