Find the general solution to y′′+2y′+5y=0y'' + 2y' + 5y = 0y′′+2y′+5y=0.
y=e−x(c1cos2x+c2sin2x)y = e^{-x}(c_1 \cos 2x + c_2 \sin 2x)y=e−x(c1cos2x+c2sin2x)
y=ex(c1cos2x+c2sin2x)y = e^{x}(c_1 \cos 2x + c_2 \sin 2x)y=ex(c1cos2x+c2sin2x)
y=c1e−x+c2e−5xy = c_1 e^{-x} + c_2 e^{-5x}y=c1e−x+c2e−5x
y=e−x(c1cos5x+c2sin5x)y = e^{-x}(c_1 \cos 5x + c_2 \sin 5x)y=e−x(c1cos5x+c2sin5x)