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

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

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

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

\[ {}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 16 t^{\frac {3}{2}} \]

\[ {}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 16 t^{\frac {3}{2}} \]

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

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

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = \frac {1}{x^{5}} \]

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+36 y = x^{2} \]

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

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

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

\[ {}9 x^{2} y^{\prime \prime }+27 x y^{\prime }+10 y = \frac {1}{x} \]

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

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

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

\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 8 x \]

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = -\frac {16 \ln \left (x \right )}{x} \]

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

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

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 2 \ln \left (x \right )^{2}+12 x \]

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = 5 x^{4} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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