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

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

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

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

\[ {}\left (x^{2}-25\right )^{2} y^{\prime \prime }-\left (x +5\right ) y^{\prime }+10 y = 0 \]

\[ {}2 x y^{\prime \prime }-5 y^{\prime }-3 y = 0 \]

\[ {}5 x y^{\prime \prime }+8 y^{\prime }-x y = 0 \]

\[ {}9 x y^{\prime \prime }+14 y^{\prime }+\left (-1+x \right ) y = 0 \]

\[ {}7 x y^{\prime \prime }+10 y^{\prime }+\left (-x^{2}+1\right ) y = 0 \]

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

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

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

\[ {}y^{\prime \prime }+\left (\frac {16}{3 x}-1\right ) y^{\prime }-\frac {16 y}{3 x^{2}} = 0 \]

\[ {}y^{\prime \prime }+\left (\frac {1}{2 x}-2\right ) y^{\prime }-\frac {35 y}{16 x^{2}} = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (16 x^{2}-25\right ) y = 0 \]

\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = 0 \]

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

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

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

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

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = 0 \]

\[ {}6 y^{\prime \prime }+5 y^{\prime }-4 y = 0 \]

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

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

\[ {}y^{\prime \prime }-10 y^{\prime }+34 y = 0 \]

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

\[ {}15 y^{\prime \prime }-11 y^{\prime }+2 y = 0 \]

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

\[ {}12 y^{\prime \prime }+8 y^{\prime }+y = 0 \]

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

\[ {}9 y^{\prime \prime \prime }+36 y^{\prime \prime }+40 y^{\prime } = 0 \]

\[ {}9 y^{\prime \prime \prime }+12 y^{\prime \prime }+13 y^{\prime } = 0 \]

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = -t \]

\[ {}y^{\prime \prime }+5 y^{\prime } = 5 t^{2} \]

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

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (2 t \right ) \]

\[ {}y^{\prime \prime }-9 y = \frac {1}{1+{\mathrm e}^{3 t}} \]

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

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = -4 \,{\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 3 \,{\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime }+9 y^{\prime }+20 y = -2 t \,{\mathrm e}^{t} \]

\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 3 t^{2} {\mathrm e}^{-4 t} \]

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }+5 y = {\mathrm e}^{t} \]

\[ {}y^{\prime \prime \prime }-12 y^{\prime }-16 y = {\mathrm e}^{4 t}-{\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+18 y^{\prime \prime }+30 y^{\prime }+25 y = {\mathrm e}^{-t} \cos \left (2 t \right )+{\mathrm e}^{-2 t} \sin \left (t \right ) \]

\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+14 y^{\prime \prime }+20 y^{\prime }+25 y = t^{2} \]

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

\[ {}y^{\prime \prime }+10 y^{\prime }+16 y = 0 \]

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

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

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

\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = {\mathrm e}^{t} \]

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

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

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

\[ {}y^{\prime \prime }+y = \csc \left (t \right ) \]

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}} \]

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}} \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+25 y = 0 \]

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

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

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

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

\[ {}3 x y^{\prime \prime }+11 y^{\prime }-y = 0 \]

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

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

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

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

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

\[ {}4 x^{\prime \prime }+9 x = 0 \]

\[ {}9 x^{\prime \prime }+4 x = 0 \]

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

\[ {}x^{\prime \prime }+100 x = 0 \]

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

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

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

\[ {}x^{\prime \prime }+256 x = 0 \]