Answer
True
Work Step by Step
The complimentary equation for the differential equation is: $$y=c_2-c_1e^{-x}$$
We can notice that $(-1+2i)$ is not the root of the complimentary equation.
We have: $R[e^{(-1+2i)x}]=e^{-x} \cos (2x)$
Therefore, the given statement is $\bf{True}$.
