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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 10 \sin \relax (t ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \]

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t^{2} & 0<t <5 \\ 0 & 5<t \end {array}\right . \]

\[ {}y^{\prime \prime }+4 y = \delta \left (-\pi +t \right ) \]

\[ {}y^{\prime \prime }+16 y = 4 \delta \left (-3 \pi +t \right ) \]

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

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -1\right ) \]

\[ {}4 y^{\prime \prime }+24 y^{\prime }+37 y = 17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right ) \]

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 10 \sin \relax (t )+10 \delta \left (t -1\right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \left (1-\theta \left (-10+t \right )\right ) {\mathrm e}^{t}-{\mathrm e}^{10} \delta \left (-10+t \right ) \]

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = \delta \left (t -\frac {\pi }{2}\right )+\theta \left (-\pi +t \right ) \cos \relax (t ) \]

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = \theta \left (t -1\right )+\delta \left (t -2\right ) \]

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 25 t -100 \delta \left (-\pi +t \right ) \]

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

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

\[ {}y^{\prime } = \sin \relax (x ) y \]

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\frac {1}{\sqrt {x}}+\frac {y^{\prime }}{\sqrt {y}} = 0 \]

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

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

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

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

\[ {}y^{\prime } = \frac {\sqrt {y}}{\sqrt {x}} \]

\[ {}y^{\prime } = \frac {\sqrt {y}}{x} \]

\[ {}z^{\prime } = 10^{x +z} \]

\[ {}x^{\prime }+t = 1 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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