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

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

\[ {}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0 \]

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

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

\[ {}2 y^{\prime \prime }-3 y^{\prime }+y = \left (t^{2}+1\right ) {\mathrm e}^{t} \]

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = t \,{\mathrm e}^{3 t}+1 \]

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

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = t^{\frac {5}{2}} {\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \sqrt {t +1} \]

\[ {}y^{\prime \prime }-y = f \left (t \right ) \]

\[ {}m y^{\prime \prime }+c y^{\prime }+k y = F_{0} \cos \left (\omega t \right ) \]

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

\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 0 \]

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]

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

\[ {}2 y^{\prime \prime }+3 y^{\prime }-2 y = 0 \]

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

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

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

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

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

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

\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime }+8 y = 0 \]

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

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 0 \]

\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }-17 y^{\prime }+60 y = 0 \]

\[ {}y^{\prime \prime \prime }-9 y^{\prime \prime }+23 y^{\prime }-15 y = 0 \]

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

\[ {}2 y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-20 y^{\prime \prime }+27 y^{\prime }+18 y = 0 \]

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

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

\[ {}4 y^{\prime \prime \prime }+2 y^{\prime \prime }-4 y^{\prime }+y = 0 \]

\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }-2 y^{\prime }+24 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-7 y^{\prime \prime }-8 y^{\prime }+12 y = 0 \]

\[ {}y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+15 y^{\prime \prime }+4 y^{\prime }-12 y = 0 \]

\[ {}y^{\left (5\right )}+y^{\prime \prime \prime \prime }-13 y^{\prime \prime \prime }-13 y^{\prime \prime }+36 y^{\prime }+36 y = 0 \]

\[ {}y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-15 y^{\prime \prime \prime }-19 y^{\prime \prime }+30 y^{\prime } = 0 \]

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

\[ {}y^{\left (5\right )}+3 y^{\prime \prime \prime }+2 y^{\prime } = 0 \]

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

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

\[ {}2 y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-3 y = 0 \]

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

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

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

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

\[ {}4 y^{\left (5\right )}-3 y^{\prime \prime \prime }-y^{\prime \prime } = 0 \]

\[ {}y^{\prime \prime \prime }-7 y^{\prime \prime }+16 y^{\prime }-12 y = 0 \]

\[ {}4 y^{\prime \prime \prime }-8 y^{\prime \prime }+5 y^{\prime }-y = 0 \]

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

\[ {}y^{\prime \prime \prime }-8 y = 0 \]

\[ {}y^{\prime \prime }-2 y^{\prime }+3 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime }-20 y = 0 \]

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

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-8 y^{\prime }+8 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-6 y^{\prime }+2 y = 0 \]

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

\[ {}2 y^{\prime \prime \prime }-3 y^{\prime \prime }+10 y^{\prime }-15 y = 0 \]

\[ {}2 y^{\prime \prime \prime }-3 y^{\prime \prime }+11 y^{\prime }-40 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-12 y^{\prime }+16 y = 0 \]

\[ {}4 y^{\prime \prime \prime }+12 y^{\prime \prime }-3 y^{\prime }+14 y = 0 \]

\[ {}y^{\left (5\right )}-y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }-6 y^{\prime \prime }+8 y^{\prime }-8 y = 0 \]

\[ {}y^{\prime \prime }-4 y = 3 \cos \left (x \right ) \]

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-y^{\prime }-6 y = x^{3} \]

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

\[ {}y^{\prime \prime }+4 y = x \sin \left (x \right ) \]

\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime } = x^{2}+8 \]

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

\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-12 y = x +{\mathrm e}^{2 x} \]

\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }-4 y = {\mathrm e}^{4 x} \sin \left (x \right ) \]

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

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

\[ {}y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y = \sin \left (k x \right ) \]

\[ {}y^{\prime \prime }+2 n y^{\prime }+n^{2} y = 5 \cos \left (6 x \right ) \]

\[ {}y^{\prime \prime }+9 y = \left (1+\sin \left (3 x \right )\right ) \cos \left (2 x \right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 2 x -{\mathrm e}^{-4 x}+\sin \left (2 x \right ) \]

\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime } = \left (2 x^{2}+x \right ) {\mathrm e}^{-2 x}+5 \cos \left (3 x \right ) \]

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

\[ {}y^{\prime \prime \prime \prime }+4 y = 5 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \]

\[ {}y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 x} \]

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

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

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

\[ {}2 y^{\prime \prime }+y^{\prime } = 8 \sin \left (2 x \right )+{\mathrm e}^{-x} \]

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

\[ {}2 y^{\prime \prime }+5 y^{\prime }-3 y = \sin \left (x \right )-8 x \]

\[ {}8 y^{\prime \prime }-y = x \,{\mathrm e}^{-\frac {x}{2}} \]

\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \]

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