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

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

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

\[ {}[x^{\prime }\left (t \right ) = -11 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 13 x \left (t \right )-9 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 7 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 10 x \left (t \right )-3 y \left (t \right )] \]

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

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

\[ {}[x^{\prime }\left (t \right ) = -3 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-5 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 13 x \left (t \right ), y^{\prime }\left (t \right ) = 13 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 7 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )] \]

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

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

\[ {}12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime } = 0 \]

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

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

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

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

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

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

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

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

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

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

\[ {}x^{\prime } = {\mathrm e}^{\frac {x}{t}}+\frac {x}{t} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = \left (x -5 y\right )^{\frac {1}{3}}+2 \]

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

\[ {}x^{\prime }+5 x = 10 t +2 \]

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

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

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

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

\[ {}x^{\prime }-x \cot \left (t \right ) = 4 \sin \left (t \right ) \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-6 y^{\prime }+10 y = 100 \]

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

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

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

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 2 \]

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

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

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

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

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

\[ {}y^{\prime \prime \prime \prime }-16 y = x^{2}-{\mathrm e}^{x} \]

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-\frac {1}{25}\right ) y = 0 \]

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

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

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

\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{r} = 0 \]

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

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

\[ {}x^{\prime \prime }+9 x = t \sin \left (3 t \right ) \]

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

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

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

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

\[ {}m x^{\prime \prime } = f \left (x\right ) \]

\[ {}m x^{\prime \prime } = f \left (x^{\prime }\right ) \]

\[ {}y^{\left (6\right )}-3 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-y^{\prime \prime \prime } = x \]

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

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

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

\[ {}x^{\prime \prime \prime \prime }+x = t^{3} \]

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

\[ {}x^{\prime \prime }+10 x^{\prime }+25 x = 2^{t}+t \,{\mathrm e}^{-5 t} \]

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