10. Determine which are the values of the parameter $k \in \mathbb{R}$ for which the function $y(x) = 2e^{kx+2}$ is a solution of the differential equation $y'' - 2y' - 3y = 0$.
\footnotetext{Maximum duration of the examination: 6 hours. The use of scientific and/or graphical calculators is permitted provided they are not equipped with symbolic calculation capacity (O.M. no. 350 Art. 18 paragraph 8). The use of a bilingual dictionary (Italian–language of the country of origin) is permitted for candidates whose native language is not Italian. It is not permitted to leave the Institute before 3 hours have elapsed from the dictation of the theme.}