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

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

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

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{3} = 0 \]

\[ {}4 x^{2} y^{\prime \prime }+y = 8 \sqrt {x}\, \left (\ln \left (x \right )+1\right ) \]

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

\[ {}\frac {x y^{\prime \prime }}{1-x}+x y = 0 \]

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

\[ {}\frac {x y^{\prime \prime }}{-x^{2}+1}+y = 0 \]

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

\[ {}y^{\prime \prime }+20 y^{\prime }+500 y = 100000 \cos \left (100 x \right ) \]

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x} \]

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

\[ {}y^{\prime \prime }+2 y^{\prime }-24 y = 16-\left (2+x \right ) {\mathrm e}^{4 x} \]

\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -2} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y {y^{\prime \prime }}^{3}+y^{3} {y^{\prime }}^{5} = 0 \]

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

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

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

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

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

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

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

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

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

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

\[ {}10 y^{\prime \prime }+x^{2} y^{\prime }+\frac {3 {y^{\prime }}^{2}}{y} = 0 \]

\[ {}10 y^{\prime \prime }+\left ({\mathrm e}^{x}+3 x \right ) y^{\prime }+\frac {3 \,{\mathrm e}^{y} {y^{\prime }}^{2}}{\sin \left (y\right )} = 0 \]

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

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

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

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

\[ {}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}} \]

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

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

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 4 \cos \left (\ln \left (1+x \right )\right ) \]

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

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

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

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

\[ {}y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x} = 4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x} \]

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