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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x y^{\prime \prime }-3 y^{\prime } = 5 x \]

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

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

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

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

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

\[ {}y^{\prime \prime }-9 y^{\prime }+20 y = 0 \]

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

\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

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

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

\[ {}4 y^{\prime \prime }+20 y^{\prime }+25 y = 0 \]

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

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

\[ {}4 y^{\prime \prime }-8 y^{\prime }+7 y = 0 \]

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+8 y^{\prime }-9 y = 0 \]

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+10 y = 0 \]

\[ {}2 x^{2} y^{\prime \prime }+10 x y^{\prime }+8 y = 0 \]

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \]

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 0 \]

\[ {}y^{\prime \prime }+3 y^{\prime }-10 y = 6 \,{\mathrm e}^{4 x} \]

\[ {}y^{\prime \prime }+4 y = 3 \sin \relax (x ) \]

\[ {}y^{\prime \prime }+10 y^{\prime }+25 y = 14 \,{\mathrm e}^{-5 x} \]

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 25 x^{2}+12 \]

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 20 \,{\mathrm e}^{-2 x} \]

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \]

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

\[ {}y^{\prime \prime }-2 y^{\prime } = 12 x -10 \]

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

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

\[ {}y^{\prime \prime }+y^{\prime } = 10 x^{4}+2 \]

\[ {}y^{\prime \prime }+4 y = 4 \cos \left (2 x \right )+6 \cos \relax (x )+8 x^{2}-4 x \]

\[ {}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right )+4 \sin \relax (x )-26 \,{\mathrm e}^{-2 x}+27 x^{3} \]

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

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

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

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

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 64 x \,{\mathrm e}^{-x} \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{-x} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y = 0 \]