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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 x y^{\prime }-1 = 0 \]

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

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

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

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

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

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

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

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

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

\[ {}{y^{\prime }}^{2} x^{3}+x^{2} y y^{\prime }+1 = 0 \]

\[ {}3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}4 {y^{\prime }}^{2} = 9 x \]

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

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

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 0 \]

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

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

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

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

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

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime } = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (1+x \right )^{2} y^{\prime \prime }-\left (1+x \right ) y^{\prime }+6 y = x \]

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

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

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

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

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

\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \left (\ln \left (x \right )+1\right )^{2} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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