Question

Show that r=e^-t(c1 cos2t + c2 sin2t), where c1 and c2 are constant vectors, is a solution of the differential equation d^2r/dt^2 + 2 dr/dt + 5r = 0

Answer 1

Caracteristic equation:
\(\lambda^2+2\lambda +5=0\)
\(\lambda= \frac{-2\pm \sqrt{4-20}}{2}=-1 \pm i2\)
so the solutions will have a form:
\(r=e^{-t}(C_1 \cos2t + C_2 \sin2t), \)

Answer 2

so that's it?

Answer 3

yes

Answer 4

Other way you could just differentiate r=e^-t(c1 cos2t + c2 sin2t), and substitute it into the equation and see if it satisfies it.