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

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

\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }+\left (6 x -8\right ) y = 0 \]

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 7 x^{\frac {3}{2}} {\mathrm e}^{x} \]

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

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

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

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

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

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

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

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

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

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

\[ {}4 x^{2} y^{\prime \prime }-4 x \left (1+x \right ) y^{\prime }+\left (2 x +3\right ) y = 4 x^{\frac {5}{2}} {\mathrm e}^{2 x} \]

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 4 x^{2} \]

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

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

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

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

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

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

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

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

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

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \]

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

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

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

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

\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }-\left (6 x -8\right ) y = 0 \]

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

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

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

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

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

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

\[ {}y^{\prime }+y^{2}+8 y+7 = 0 \]

\[ {}y^{\prime }+y^{2}+14 y+50 = 0 \]

\[ {}6 y^{\prime }+6 y^{2}-y-1 = 0 \]

\[ {}36 y^{\prime }+36 y^{2}-12 y+1 = 0 \]

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

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

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

\[ {}\left (3 x -1\right ) \left (y^{\prime }+y^{2}\right )-\left (2+3 x \right ) y-6 x +8 = 0 \]

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

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

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

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

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \frac {4}{1+{\mathrm e}^{-x}} \]

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 3 \,{\mathrm e}^{x} \sec \relax (x ) \]

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 14 x^{\frac {3}{2}} {\mathrm e}^{x} \]

\[ {}y^{\prime \prime }-y = \frac {4 \,{\mathrm e}^{-x}}{1-{\mathrm e}^{-2 x}} \]

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{\frac {5}{2}} \]

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 2 x^{4} \sin \relax (x ) \]

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

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

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

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

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

\[ {}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = 8 x^{5} \]

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

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 8 x^{\frac {5}{2}} \]

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}+3\right ) y = x^{\frac {7}{2}} \]

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

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

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

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

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

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

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

\[ {}4 x^{2} y^{\prime \prime }-4 x \left (1+x \right ) y^{\prime }+\left (2 x +3\right ) y = x^{\frac {5}{2}} {\mathrm e}^{x} \]

\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }-\left (6 x -8\right ) y = \left (3 x -1\right )^{2} {\mathrm e}^{2 x} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (1+2 x \right ) y^{\prime }-\left (4+6 x \right ) y = 0 \]