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

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

\[ {}y^{\prime \prime }+9 y = 7 \sin \left (4 t \right )+14 \cos \left (4 t \right ) \]

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

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

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 1-3 \operatorname {Heaviside}\left (t -2\right ) \]

\[ {}y^{\prime \prime }-4 y = \operatorname {Heaviside}\left (-1+t \right )-\operatorname {Heaviside}\left (t -2\right ) \]

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

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = -10 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \cos \left (t +\frac {\pi }{4}\right ) \]

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 30 \operatorname {Heaviside}\left (-1+t \right ) {\mathrm e}^{1-t} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 5 \operatorname {Heaviside}\left (t -3\right ) \]

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 2 \sin \left (t \right )+\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (1+\cos \left (t \right )\right ) \]

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

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

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

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right ) \]

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

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right ) \]

\[ {}y^{\prime \prime }+9 y = 15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right ) \]

\[ {}y^{\prime \prime }+16 y = 4 \cos \left (3 t \right )+\delta \left (t -\frac {\pi }{3}\right ) \]

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \sin \left (t \right )+\delta \left (t -\frac {\pi }{6}\right ) \]

\[ {}y^{\prime \prime }+6 y^{\prime }+10 y = 3 x \,{\mathrm e}^{-3 x}-2 \,{\mathrm e}^{3 x} \cos \left (x \right ) \]

\[ {}y^{\prime \prime }-8 y^{\prime }+17 y = {\mathrm e}^{4 x} \left (x^{2}-3 x \sin \left (x \right )\right ) \]

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

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

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

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

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

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

\[ {}6 y^{\prime \prime }-11 y^{\prime }+4 y = 0 \]

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

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

\[ {}y^{\prime \prime }+4 k y^{\prime }-12 k^{2} y = 0 \]

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

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

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

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

\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = 0 \]

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

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

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

\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = 0 \]

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

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

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

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

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

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right ) \]

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

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+9 y = 8 \cos \left (x \right ) \]

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{x} \left (2 x -3\right ) \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{3} y^{\prime \prime } = k \]

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

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

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

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

\[ {}r^{\prime \prime } = -\frac {k}{r^{2}} \]

\[ {}y^{\prime \prime } = \frac {3 k y^{2}}{2} \]

\[ {}y^{\prime \prime } = 2 k y^{3} \]

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

\[ {}r^{\prime \prime } = \frac {h^{2}}{r^{3}}-\frac {k}{r^{2}} \]

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

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