\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = \left (2 x^{2}+4 x +8\right ) \cos \left (x \right )+\left (6 x^{2}+8 x +12\right ) \sin \left (x \right ) \]

\[ {}y^{\left (6\right )}-12 y^{\left (5\right )}+63 y^{\prime \prime \prime \prime }-18 y^{\prime \prime \prime }+315 y^{\prime \prime }-300 y^{\prime }+125 y = {\mathrm e}^{x} \left (48 \cos \left (x \right )+96 \sin \left (x \right )\right ) \]

\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime }-y = 0 \]

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 2 \,{\mathrm e}^{x} \]

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3 x +4 \]

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \]

\[ {}y^{\prime \prime }-9 y = 2 \sin \left (3 x \right ) \]

\[ {}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right ) \]

\[ {}y^{\prime \prime }+y^{\prime }-2 y = x \,{\mathrm e}^{x}-3 x^{2} \]

\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime } = x \,{\mathrm e}^{x}-3 x^{2} \]

\[ {}y^{\prime \prime }-9 y = 2+x \]

\[ {}y^{\prime \prime }+9 y = 2+x \]

\[ {}y^{\prime \prime }-y^{\prime }+6 y = -2 \sin \left (3 x \right ) \]

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = -x^{2}+1 \]

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = x +\cos \left (x \right ) \]

\[ {}y^{\prime \prime }+9 y = 1 \]

\[ {}y^{\prime \prime }+9 y = 18 \,{\mathrm e}^{3 x} \]

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \]

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

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \sin \left (x \right ) \]

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y = 0 \]

\[ {}y^{\prime \prime }-y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & 2\le x <4 \\ 0 & \operatorname {otherwise} \end {array}\right . \]

\[ {}y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ \left (-1+x \right )^{2} & 1\le x \end {array}\right . \]

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ x^{2}-2 x +3 & 1\le x \end {array}\right . \]

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le x <\pi \\ -\sin \left (3 x \right ) & \pi \le x \end {array}\right . \]

\[ {}y^{\prime \prime }-4 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \]

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \]

\[ {}y^{\prime \prime }+9 y = \delta \left (x -\pi \right )+\delta \left (x -3 \pi \right ) \]

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \delta \left (-1+x \right ) \]

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = \cos \left (x \right )+2 \delta \left (x -\pi \right ) \]

\[ {}y^{\prime \prime }+4 y = \cos \left (x \right ) \delta \left (x -\pi \right ) \]

\[ {}y^{\prime \prime }+a^{2} y = \delta \left (x -\pi \right ) f \left (x \right ) \]

\[ {}y^{\prime \prime }-6 y^{\prime }-7 y = 0 \]

\[ {}y^{\prime \prime }-y^{\prime }-12 y = 0 \]

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 0 \]

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]

\[ {}y^{\prime \prime }+2 y = 0 \]

\[ {}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{4 t} \]

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \,{\mathrm e}^{-3 t} \]

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{3 t} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = {\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = {\mathrm e}^{4 t} \]

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 4 \,{\mathrm e}^{-3 t} \]

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 3 \,{\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-\frac {t}{2}} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-4 t} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-\frac {t}{2}} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-4 t} \]

\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = 5 \]

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 2 \]

\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 10 \]

\[ {}y^{\prime \prime }+4 y^{\prime }+6 y = -8 \]

\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }+4 y = 2 \,{\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime }+2 y = -3 \]

\[ {}y^{\prime \prime }+4 y = {\mathrm e}^{t} \]

\[ {}y^{\prime \prime }+9 y = 6 \]

\[ {}y^{\prime \prime }+2 y = -{\mathrm e}^{t} \]

\[ {}y^{\prime \prime }+4 y = -3 t^{2}+2 t +3 \]

\[ {}y^{\prime \prime }+2 y^{\prime } = 3 t +2 \]

\[ {}y^{\prime \prime }+4 y^{\prime } = 3 t +2 \]

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = t^{2} \]

\[ {}y^{\prime \prime }+4 y = t -\frac {1}{20} t^{2} \]

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 4+{\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-t}-4 \]

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{t} \]

\[ {}y^{\prime \prime }+4 y = t +{\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }+4 y = 6+t^{2}+{\mathrm e}^{t} \]

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (t \right ) \]

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 5 \cos \left (t \right ) \]

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (t \right ) \]

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 2 \sin \left (t \right ) \]

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right ) \]

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = -4 \cos \left (3 t \right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 3 \cos \left (2 t \right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = -\cos \left (5 t \right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = -3 \sin \left (2 t \right ) \]

\[ {}y^{\prime \prime }+2 y^{\prime }+y = \cos \left (3 t \right ) \]

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right ) \]

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \cos \left (3 t \right ) \]

\[ {}y^{\prime \prime }+6 y^{\prime }+20 y = -3 \sin \left (2 t \right ) \]

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

\[ {}y^{\prime \prime }+3 y^{\prime }+y = \cos \left (3 t \right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = 3+2 \cos \left (2 t \right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-t} \cos \left (t \right ) \]

\[ {}y^{\prime \prime }+9 y = \cos \left (t \right ) \]

\[ {}y^{\prime \prime }+9 y = 5 \sin \left (2 t \right ) \]

\[ {}y^{\prime \prime }+4 y = -\cos \left (\frac {t}{2}\right ) \]

\[ {}y^{\prime \prime }+4 y = 3 \cos \left (2 t \right ) \]