\[ {}y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} \sin \left (3 x \right ) \]

\[ {}y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} {\mathrm e}^{3 x} \sin \left (3 x \right ) \]

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 30 x \cos \left (2 x \right ) \]

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

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

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 5 x^{5} {\mathrm e}^{2 x} \]

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 27 \,{\mathrm e}^{6 x}+25 \sin \left (6 x \right ) \]

\[ {}y^{\prime \prime }+9 y = 25 x \cos \left (2 x \right )+3 \sin \left (3 x \right ) \]

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

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

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

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

\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = 6 \,{\mathrm e}^{3 x} \]

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = \left (24 x^{2}+2\right ) {\mathrm e}^{2 x} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 x}}{x^{2}+1} \]

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 12 \,{\mathrm e}^{2 x} \]

\[ {}y^{\prime \prime \prime }-4 y^{\prime } = 30 \,{\mathrm e}^{3 x} \]

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

\[ {}y^{\prime \prime \prime \prime }-81 y = \sinh \left (x \right ) \]

\[ {}y^{\prime \prime }+36 y = 0 \]

\[ {}y^{\prime \prime }-12 y^{\prime }+36 y = 0 \]

\[ {}y^{\prime \prime }-36 y = 0 \]

\[ {}y^{\prime \prime }-9 y^{\prime }+14 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y = 0 \]

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

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

\[ {}y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+13 y^{\prime \prime \prime } = 0 \]

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 0 \]

\[ {}y^{\prime \prime }-8 y^{\prime }+25 y = 0 \]

\[ {}y^{\prime \prime }+y^{\prime }-30 y = 0 \]

\[ {}16 y^{\prime \prime }-8 y^{\prime }+y = 0 \]

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime } = 8 \]

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

\[ {}2 y^{\prime \prime }-7 y^{\prime }+3 = 0 \]

\[ {}y^{\prime \prime }+20 y^{\prime }+100 y = 0 \]

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

\[ {}y^{\prime \prime }-9 y^{\prime }+14 y = 98 x^{2} \]

\[ {}y^{\prime \prime }-12 y^{\prime }+36 y = 25 \sin \left (3 x \right ) \]

\[ {}y^{\prime \prime }-9 y^{\prime }+14 y = 576 x^{2} {\mathrm e}^{-x} \]

\[ {}y^{\prime \prime }-12 y^{\prime }+36 y = 81 \,{\mathrm e}^{3 x} \]

\[ {}y^{\prime \prime }-12 y^{\prime }+36 y = 3 x \,{\mathrm e}^{6 x}-2 \,{\mathrm e}^{6 x} \]

\[ {}y^{\prime \prime }+36 y = 6 \sec \left (6 x \right ) \]

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 10 \,{\mathrm e}^{-3 x} \]

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 2 \cos \left (2 x \right ) \]

\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = x \,{\mathrm e}^{\frac {3 x}{2}} \]

\[ {}3 y^{\prime \prime }+8 y^{\prime }-3 y = 123 \sin \left (3 x \right ) x \]

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

\[ {}y^{\left (6\right )}-64 y = {\mathrm e}^{-2 x} \]

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

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

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

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

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

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = t^{2} {\mathrm e}^{4 t} \]

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 7 \]

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 4 t +2 \,{\mathrm e}^{2 t} \sin \left (3 t \right ) \]

\[ {}y^{\prime \prime \prime }-27 y = {\mathrm e}^{-3 t} \]

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

\[ {}y^{\prime \prime }+9 y = 27 t^{3} \]

\[ {}y^{\prime \prime }+8 y^{\prime }+7 y = 165 \,{\mathrm e}^{4 t} \]

\[ {}y^{\prime \prime }-8 y^{\prime }+17 y = 0 \]

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = t^{2} {\mathrm e}^{3 t} \]

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 0 \]

\[ {}y^{\prime \prime }+8 y^{\prime }+17 y = 0 \]

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

\[ {}y^{\prime \prime }-4 y^{\prime }+40 y = 122 \,{\mathrm e}^{-3 t} \]

\[ {}y^{\prime \prime }-9 y = 24 \,{\mathrm e}^{-3 t} \]

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right ) \]

\[ {}y^{\prime \prime }+4 y = 1 \]

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

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

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

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

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 1 \]

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

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 t} \]

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{-3 t} \]

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{t} \]

\[ {}y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right ) \]

\[ {}y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right ) \]

\[ {}y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -10\right ) \]

\[ {}y^{\prime \prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \]

\[ {}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \]

\[ {}y^{\prime \prime } = \delta \left (t -3\right ) \]

\[ {}y^{\prime \prime } = \delta \left (-1+t \right )-\delta \left (t -4\right ) \]

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

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

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

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

\[ {}y^{\prime \prime }+16 y = \delta \left (t -2\right ) \]

\[ {}y^{\prime \prime }-16 y = \delta \left (t -10\right ) \]

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

\[ {}y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t \right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t -3\right ) \]

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = \delta \left (t -4\right ) \]

\[ {}y^{\prime \prime }-12 y^{\prime }+45 y = \delta \left (t \right ) \]

\[ {}y^{\prime \prime \prime }+9 y^{\prime } = \delta \left (-1+t \right ) \]

\[ {}y^{\prime \prime \prime \prime }-16 y = \delta \left (t \right ) \]

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