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

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

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

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

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

\[ {}4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y = 0 \]

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

\[ {}9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (x^{6}-36\right ) y = 0 \]

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

\[ {}x y^{\prime \prime }+y^{\prime }-7 y x^{3} = 0 \]

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

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

\[ {}16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y = 0 \]

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {4}{49}\right ) y = 0 \]

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

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

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

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

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

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

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

\[ {}9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (36 x^{4}-16\right ) y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime }+\frac {26 y}{5} = \frac {97 \sin \left (2 t \right )}{5} \]

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

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

\[ {}y^{\prime \prime }+9 y = 10 \,{\mathrm e}^{-t} \]

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

\[ {}y^{\prime \prime }-6 y^{\prime }+5 y = 29 \cos \left (2 t \right ) \]

\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 21 \,{\mathrm e}^{3 t} \]

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

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 6 t -8 \]

\[ {}y^{\prime \prime }+\frac {y}{25} = \frac {t^{2}}{50} \]

\[ {}y^{\prime \prime }+3 y^{\prime }+\frac {9 y}{4} = 9 t^{3}+64 \]

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

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

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 50 t -100 \]

\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -3} \]

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

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-3 t}-{\mathrm e}^{-5 t} \]

\[ {}y^{\prime \prime }+10 y^{\prime }+24 y = 144 t^{2} \]

\[ {}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right . \]

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right . \]

\[ {}y^{\prime \prime }+y^{\prime }-2 y = \left \{\begin {array}{cc} 3 \sin \left (t \right )-\cos \left (t \right ) & 0<t <2 \pi \\ 3 \sin \left (2 t \right )-\cos \left (2 t \right ) & 2 \pi <t \end {array}\right . \]

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0<t <1 \\ 0 & 1<t \end {array}\right . \]