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

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

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

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

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

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

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

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

\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (1+x \right ) y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-9 x y^{\prime }+25 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}\frac {x y^{\prime \prime }}{1-x}+y = \cos \relax (x ) \]

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

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

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

\[ {}[x^{\prime }\relax (t ) = x \relax (t )+2 y \relax (t )+2 t +1, y^{\prime }\relax (t ) = 5 x \relax (t )+y \relax (t )+3 t -1] \]

\[ {}y^{\prime \prime }+20 y^{\prime }+500 y = 100000 \cos \left (100 x \right ) \]

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

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

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

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

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

\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x} \]

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

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

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

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

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

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

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

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

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

\[ {}h^{2}+\frac {2 a h}{\sqrt {1+\left (h^{\prime }\right )^{2}}} = b^{2} \]

\[ {}y^{\prime \prime }+2 y^{\prime }-24 y = 16-\left (2+x \right ) {\mathrm e}^{4 x} \]

\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -2} \]

\[ {}y^{\prime \prime }+y = {\mathrm e}^{a \cos \relax (x )} \]

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = a x \]

\[ {}y^{\prime } = y a x \]

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

\[ {}y^{\prime } = a x +b y \]

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

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

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

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

\[ {}c y^{\prime } = a \]

\[ {}c y^{\prime } = a x \]

\[ {}c y^{\prime } = a x +y \]

\[ {}c y^{\prime } = a x +b y \]

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

\[ {}c y^{\prime } = b y \]

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

\[ {}c y^{\prime } = \frac {a x +b y^{2}}{r} \]

\[ {}c y^{\prime } = \frac {a x +b y^{2}}{r x} \]

\[ {}c y^{\prime } = \frac {a x +b y^{2}}{r \,x^{2}} \]

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

\[ {}a \sin \relax (x ) y x y^{\prime } = 0 \]

\[ {}f \relax (x ) \sin \relax (x ) y x y^{\prime } \pi = 0 \]

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

\[ {}y^{\prime } = \sin \relax (x )+y^{2} \]

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

\[ {}y^{\prime } = \cos \relax (x )+\frac {y^{2}}{x} \]

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

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

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

\[ {}{\mathrm e} y^{\prime } = 0 \]

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

\[ {}\sin \relax (x ) y^{\prime } = 0 \]

\[ {}f \relax (x ) y^{\prime } = 0 \]

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