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

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

\[ {}6 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2} = 0 \]

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

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

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

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

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

\[ {}[x^{\prime }\left (t \right )+5 x \left (t \right )+y \left (t \right ) = {\mathrm e}^{t}, y^{\prime }\left (t \right )-x \left (t \right )-3 y \left (t \right ) = {\mathrm e}^{2 t}] \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}5 y^{\prime }-x y = 0 \]

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

\[ {}2 y^{\prime \prime }+3 y^{\prime }+4 x^{2} y = 1 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\sin \left (x \right ) y^{\prime \prime }+x y^{\prime }+7 y = 1 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x y^{\prime \prime }+\left (6 x y^{2}+1\right ) y^{\prime }+2 y^{3}+1 = 0 \]

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

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

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

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

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

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

\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime } = \left (25-6 x \right ) y \]

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

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

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

\[ {}\left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime \prime }+\left (7 \sin \left (x \right )+4 \cos \left (x \right )\right ) y^{\prime }+10 \cos \left (x \right ) y = 0 \]

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

\[ {}y^{\prime \prime }+\left (2 x +5\right ) y^{\prime }+\left (4 x +8\right ) y = {\mathrm e}^{-2 x} \]

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

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

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

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

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

\[ {}4 y^{\prime \prime }-4 y^{\prime }+37 y = 0 \]

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

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

\[ {}4 y^{\prime \prime }-12 y^{\prime }+13 y = 0 \]

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 0 \]

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

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

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

\[ {}y^{\prime \prime }-20 y^{\prime }+51 y = 0 \]

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

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

\[ {}2 y^{\prime \prime }+20 y^{\prime }+51 y = 0 \]

\[ {}4 y^{\prime \prime }+40 y^{\prime }+101 y = 0 \]