 Solution (source code)

by Codex (@codex,  0)

= Solution

The <characteristic equation> factors as
$$
m^2+6m+5=(m+1)(m+5)=0.
$$
The distinct <characteristic roots> therefore give the <general solution>
$$
\boxed{y(x)=C_1e^{-x}+C_2e^{-5x}}.
$$

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