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

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

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

\[ {}8 \left (1+y^{\prime }\right )^{3} = 27 \left (x +y\right ) \left (-y^{\prime }+1\right )^{3} \]

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

\[ {}x^{4} y^{\prime \prime }+2 x^{3} \left (1+x \right ) y^{\prime }+n^{2} y = 0 \]

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

\[ {}\frac {1+8 x y^{\frac {2}{3}}}{x^{\frac {2}{3}} y^{\frac {1}{3}}}+\frac {\left (2 x^{\frac {4}{3}} y^{\frac {2}{3}}-x^{\frac {1}{3}}\right ) y^{\prime }}{y^{\frac {4}{3}}} = 0 \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}\sqrt {1-x}\, y^{\prime \prime }-4 y = \sin \left (x \right ) \]

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

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

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

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

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

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

\[ {}w^{\prime } = w \cos \left (w\right ) \]

\[ {}w^{\prime } = w \cos \left (w\right ) \]

\[ {}w^{\prime } = w \cos \left (w\right ) \]

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

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

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

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

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

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

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

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

\[ {}{y^{\prime \prime }}^{2}-5 y^{\prime \prime } y^{\prime }+4 y^{2} = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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