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

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

\[ {}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 16 t^{\frac {3}{2}} \]

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}} \]

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

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

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

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

\[ {}x^{3} y^{\prime }-\sin \left (y\right ) = 1 \]

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

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

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

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

\[ {}3 x^{2} \tan \left (y\right )-\frac {2 y^{3}}{x^{3}}+\left (x^{3} \sec \left (y\right )^{2}+4 y^{3}+\frac {3 y^{2}}{x^{2}}\right ) y^{\prime } = 0 \]

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

\[ {}\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0 \]

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

\[ {}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0 \]

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

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

\[ {}8 {y^{\prime }}^{3}-12 {y^{\prime }}^{2} = 27 y-27 x \]

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

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

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

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

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 8 \,{\mathrm e}^{x}+9 \]

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 2 \,{\mathrm e}^{x} \left (\sin \left (x \right )+7 \cos \left (x \right )\right ) \]

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{-2 x} \left (9 \sin \left (2 x \right )+4 \cos \left (2 x \right )\right ) \]

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right ) \]

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

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

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

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

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

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

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

\[ {}\left [x^{\prime }\left (t \right ) = \frac {t +y \left (t \right )}{y \left (t \right )+x \left (t \right )}, y^{\prime }\left (t \right ) = \frac {t +x \left (t \right )}{y \left (t \right )+x \left (t \right )}\right ] \]

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

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