Solution (source code)

= Solution

The <characteristic equation> has the repeated <polynomial root> $m=-2$, because both $e^{-2x}$ and $xe^{-2x}$ occur as independent solutions. Hence its <characteristic polynomial> is
$$
(m+2)^2=m^2+4m+4.
$$
Comparing constant terms gives
$$
\boxed{\gamma=4}.
$$