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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 13 \operatorname {Heaviside}\left (t -4\right ) \]

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

\[ {}y^{\prime \prime }+3 y = \operatorname {Heaviside}\left (t -4\right ) \cos \left (5 t -20\right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+9 y = 20 \operatorname {Heaviside}\left (t -2\right ) \sin \left (t -2\right ) \]

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

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

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

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

\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = \delta \left (-1+t \right )-3 \delta \left (t -4\right ) \]

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

\[ {}y^{\prime \prime }+y^{\prime }+5 y = \operatorname {Heaviside}\left (t -2\right ) \sin \left (4 t -8\right ) \]

\[ {}y^{\prime \prime }+y^{\prime }+8 y = \left (1-\operatorname {Heaviside}\left (t -4\right )\right ) \cos \left (t -4\right ) \]

\[ {}y^{\prime \prime }+y^{\prime }+3 y = \left (1-\operatorname {Heaviside}\left (t -2\right )\right ) {\mathrm e}^{-\frac {t}{10}+\frac {1}{5}} \sin \left (t -2\right ) \]

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

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

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

\[ {}y^{\prime \prime }+16 y = t \]

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

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

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

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

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

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

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

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

\[ {}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \]

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

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

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

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

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \]

\[ {}y^{\prime \prime } = 4 x \sqrt {y^{\prime }} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime } = 4 x \sqrt {y^{\prime }} \]

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

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

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

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

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

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

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

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

\[ {}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime } = 2 y^{\prime }-5 y+30 \,{\mathrm e}^{3 x} \]

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

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 0 \]

\[ {}x^{2} y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \]

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

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

\[ {}y^{\prime \prime }-\left (4+\frac {2}{x}\right ) y^{\prime }+\left (4+\frac {4}{x}\right ) y = 0 \]

\[ {}\left (1+x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \]

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

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