 Solution (source code)

by Codex (@codex,  0)

= Solution

The <complementary function> solves the associated <homogeneous linear differential equation>. Substituting $y=e^{mx}$ gives the <characteristic equation>
$$
m^2+m-6=(m-2)(m+3)=0.
$$
Its distinct <polynomial roots> give
$$
\boxed{y_{\mathrm c}(x)=C_1e^{2x}+C_2e^{-3x}}.
$$
The forcing affects the <particular solution>, which is not needed for the <complementary function>.

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