\[ {}[x^{\prime }\relax (t ) = 2 x \relax (t )+4 y \relax (t ), y^{\prime }\relax (t ) = -x \relax (t )+6 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = z \relax (t ), y^{\prime }\relax (t ) = y \relax (t ), z^{\prime }\relax (t ) = x \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 6 x \relax (t )-y \relax (t ), y^{\prime }\relax (t ) = 5 x \relax (t )+2 y \relax (t )] \]

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

\[ {}[x^{\prime }\relax (t ) = 5 x \relax (t )+y \relax (t ), y^{\prime }\relax (t ) = -2 x \relax (t )+3 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 4 x \relax (t )+5 y \relax (t ), y^{\prime }\relax (t ) = -2 x \relax (t )+6 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 4 x \relax (t )-5 y \relax (t ), y^{\prime }\relax (t ) = 5 x \relax (t )-4 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = x \relax (t )-8 y \relax (t ), y^{\prime }\relax (t ) = x \relax (t )-3 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = z \relax (t ), y^{\prime }\relax (t ) = -z \relax (t ), z^{\prime }\relax (t ) = y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 2 x \relax (t )+y \relax (t )+2 z \relax (t ), y^{\prime }\relax (t ) = 3 x \relax (t )+6 z \relax (t ), z^{\prime }\relax (t ) = -4 x \relax (t )-3 z \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = x \relax (t )-12 y \relax (t )-14 z \relax (t ), y^{\prime }\relax (t ) = x \relax (t )+2 y \relax (t )-3 z \relax (t ), z^{\prime }\relax (t ) = x \relax (t )+y \relax (t )-2 z \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 2 x \relax (t )+3 y \relax (t )-7, y^{\prime }\relax (t ) = -x \relax (t )-2 y \relax (t )+5] \]

\[ {}[x^{\prime }\relax (t ) = 5 x \relax (t )+9 y \relax (t )+2, y^{\prime }\relax (t ) = -x \relax (t )+11 y \relax (t )+6] \]

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

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

\[ {}x^{2} \left (y^{\prime }\right )^{2}-5 x y y^{\prime }+6 y^{2} = 0 \]

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

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

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

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

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

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

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

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

\[ {}\left (4 x -y\right ) \left (y^{\prime }\right )^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (y^{\prime }\right )^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0 \]

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

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

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

\[ {}y^{4} \left (y^{\prime }\right )^{3}-6 x y^{\prime }+2 y = 0 \]

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

\[ {}\left (y^{\prime }\right )^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0 \]

\[ {}2 x \left (y^{\prime }\right )^{3}-6 y \left (y^{\prime }\right )^{2}+x^{4} = 0 \]

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

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

\[ {}x^{8} \left (y^{\prime }\right )^{2}+3 x y^{\prime }+9 y = 0 \]

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

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

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

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

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

\[ {}x^{6} \left (y^{\prime }\right )^{3}-3 x y^{\prime }-3 y = 0 \]

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

\[ {}x \left (y^{\prime }\right )^{4}-2 y \left (y^{\prime }\right )^{3}+12 x^{3} = 0 \]

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

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

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

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

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

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

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

\[ {}5 \left (y^{\prime }\right )^{2}+6 x y^{\prime }-2 y = 0 \]

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

\[ {}5 \left (y^{\prime }\right )^{2}+3 x y^{\prime }-y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\cos \relax (x ) y^{\prime \prime } = y^{\prime } \]

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y y^{\prime \prime } = \left (y^{\prime }\right )^{2} \left (1-y^{\prime } \sin \relax (y)-y y^{\prime } \cos \relax (y)\right ) \]

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

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

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

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

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