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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 8 x^{4} \]

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

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 2 x^{3} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y = \frac {1}{x^{3}} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}p \,x^{2} u^{\prime \prime }+q x u^{\prime }+r u = f \left (x \right ) \]

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = x^{2} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}2 y^{\prime \prime }+t y^{\prime }-2 y = 10 \]

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{5}+24 = 0 \]

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

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

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

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

\[ {}y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2} = 0 \]

\[ {}y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{3} = 0 \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }-y^{\prime }-x y-x^{3}+1 = 0 \]

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

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

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

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

\[ {}y^{\prime \prime }-6 y^{\prime }-x y-x^{3}+2 = 0 \]

\[ {}y^{\prime \prime }-8 y^{\prime }-x y-x^{3}+2 = 0 \]

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

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

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

\[ {}y^{\prime \prime }-x y-x^{6}+64 = 0 \]

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

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

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

\[ {}y^{\prime \prime }-x y-x^{6}-x^{3}+42 = 0 \]