\[ {}x^{\prime \prime }-x^{\prime } = 1 \]

\[ {}x^{\prime \prime }+x = t \]

\[ {}x^{\prime \prime }+6 x^{\prime } = 12 t +2 \]

\[ {}x^{\prime \prime }-2 x^{\prime }+2 x = 2 \]

\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = 4 \]

\[ {}2 x^{\prime \prime }-2 x^{\prime } = \left (t +1\right ) {\mathrm e}^{t} \]

\[ {}x^{\prime \prime }+x = 2 \cos \left (t \right ) \]