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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 3 \sqrt {x} \]

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

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

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 18 \ln \left (x \right ) \]

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

\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }-2 y = 10 x^{2} \]

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

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y = 6 \]

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{x} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = -{\mathrm e}^{-9 t} \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}5 y^{\prime \prime }+y^{\prime }-4 y = -3 \]

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 32 t \]

\[ {}16 y^{\prime \prime }-8 y^{\prime }-15 y = 75 t \]

\[ {}y^{\prime \prime }+2 y^{\prime }+26 y = -338 t \]

\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = -32 t^{2} \]

\[ {}8 y^{\prime \prime }+6 y^{\prime }+y = 5 t^{2} \]

\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = -256 t^{3} \]

\[ {}y^{\prime \prime }-2 y^{\prime } = 52 \sin \left (3 t \right ) \]

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 25 \sin \left (2 t \right ) \]

\[ {}y^{\prime \prime }-9 y = 54 t \sin \left (2 t \right ) \]

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = -78 \cos \left (3 t \right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = -32 t^{2} \cos \left (2 t \right ) \]

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

\[ {}y^{\prime \prime }-4 y^{\prime }-5 y = -648 t^{2} {\mathrm e}^{5 t} \]

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = -2 t^{3} {\mathrm e}^{4 t} \]

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

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

\[ {}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \]

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

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