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

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

\[ {}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y = 0 \]

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

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

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

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

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

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

\[ {}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+5 y^{\prime }-2 y = x \,{\mathrm e}^{x}+3 \,{\mathrm e}^{-2 x} \]

\[ {}x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y = 0 \]

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

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

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

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

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

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

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

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \]

\[ {}\left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y = 0 \]

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y = 0 \]

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

\[ {}5 y^{\prime \prime }-2 x y^{\prime }+10 y = 0 \]

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

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

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

\[ {}\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y = 0 \]

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }-12 y = 0 \]

\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0 \]

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }-4 y = 0 \]

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y = 0 \]

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

\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }-9 x y^{\prime }-6 y = 0 \]

\[ {}\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (-2+x \right ) y^{\prime }+36 y = 0 \]

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

\[ {}\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y = 0 \]

\[ {}\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (1+x \right ) y^{\prime }+60 y = 0 \]

\[ {}\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 x y = 0 \]

\[ {}\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0 \]

\[ {}y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y = 0 \]

\[ {}\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0 \]