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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}10 x^{\prime \prime }+\frac {x}{10} = 0 \]

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

\[ {}\frac {x^{\prime \prime }}{32}+2 x^{\prime }+x = 0 \]

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

\[ {}4 x^{\prime \prime }+2 x^{\prime }+8 x = 0 \]

\[ {}x^{\prime \prime }+4 x^{\prime }+13 x = 0 \]

\[ {}x^{\prime \prime }+4 x^{\prime }+20 x = 0 \]

\[ {}x^{\prime \prime }+x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]

\[ {}x^{\prime \prime }+x = \left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]

\[ {}x^{\prime \prime }+x = \left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t \end {array}\right . \]

\[ {}x^{\prime \prime }+4 x^{\prime }+13 x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 1-t & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \]

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

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

\[ {}x^{\prime \prime }+x = \cos \left (\frac {9 t}{10}\right ) \]

\[ {}x^{\prime \prime }+x = \cos \left (\frac {7 t}{10}\right ) \]

\[ {}x^{\prime \prime }+\frac {x^{\prime }}{10}+x = 3 \cos \left (2 t \right ) \]

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

\[ {}x^{\prime \prime }+6 x^{\prime }+9 x = 0 \]

\[ {}x^{\prime \prime }+16 x = t \sin \left (t \right ) \]