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

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

\[ {}y^{\prime \prime }+4 k y^{\prime }-12 k^{2} y = 0 \]

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x} \]

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

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

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

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right ) \]

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

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x} \]

\[ {}y^{\prime \prime }-3 y^{\prime } = 2 \,{\mathrm e}^{2 x} \sin \left (x \right ) \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 x} \]

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

\[ {}y^{\prime \prime }+9 y = 8 \cos \left (x \right ) \]

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{x} \left (2 x -3\right ) \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}u^{\prime \prime }-\frac {a^{2} u}{x^{\frac {2}{3}}} = 0 \]

\[ {}u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0 \]

\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u = 0 \]

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-4 y^{\prime } = 10 \]

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 16 \]

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

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 24 \,{\mathrm e}^{-3 x} \]

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

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 12 \,{\mathrm e}^{-x} \]

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

\[ {}y^{\prime \prime }-16 y = 40 \,{\mathrm e}^{4 x} \]

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