\[ {}y^{\prime \prime }-y^{\prime }-12 y = 0 \]

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

\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = 0 \]

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

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

\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

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

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

\[ {}y^{\prime \prime }-4 y^{\prime }+29 y = 0 \]

\[ {}y^{\prime \prime }+6 y^{\prime }+58 y = 0 \]

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 0 \]

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

\[ {}9 y^{\prime \prime }+6 y^{\prime }+5 y = 0 \]

\[ {}4 y^{\prime \prime }+4 y^{\prime }+37 y = 0 \]

\[ {}y^{\prime \prime }-3 y^{\prime }+8 y = 4 x^{2} \]

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 4 \,{\mathrm e}^{2 x}-21 \,{\mathrm e}^{-3 x} \]

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 6 \sin \left (2 x \right )+7 \cos \left (2 x \right ) \]

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 10 \sin \left (4 x \right ) \]

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

\[ {}y^{\prime \prime }-3 y^{\prime }-4 y = 16 x -12 \,{\mathrm e}^{2 x} \]

\[ {}y^{\prime \prime }+6 y^{\prime }+5 y = 2 \,{\mathrm e}^{x}+10 \,{\mathrm e}^{5 x} \]

\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 5 \,{\mathrm e}^{-2 x} x \]

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 10 \,{\mathrm e}^{2 x}-18 \,{\mathrm e}^{3 x}-6 x -11 \]

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

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

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

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4 \]

\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 16 x +20 \,{\mathrm e}^{x} \]

\[ {}y^{\prime \prime }-8 y^{\prime }+15 y = 9 \,{\mathrm e}^{2 x} x \]

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = 4 x \,{\mathrm e}^{-3 x} \]

\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = 8 \,{\mathrm e}^{-2 x} \]

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 27 \,{\mathrm e}^{-6 x} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 18 \,{\mathrm e}^{-2 x} \]

\[ {}y^{\prime \prime }-10 y^{\prime }+29 y = 8 \,{\mathrm e}^{5 x} \]

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 8 \sin \left (3 x \right ) \]

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 8 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x} \]

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

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

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

\[ {}y^{\prime \prime }+4 y = 8 \sin \left (2 x \right ) \]

\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = x^{3}+x +{\mathrm e}^{-2 x} \]

\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{3 x}+{\mathrm e}^{-3 x}+{\mathrm e}^{3 x} \sin \left (3 x \right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = {\mathrm e}^{-2 x} \left (\cos \left (x \right )+1\right ) \]

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = x^{4} {\mathrm e}^{x}+x^{3} {\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \]

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = x \,{\mathrm e}^{-3 x} \sin \left (2 x \right )+x^{2} {\mathrm e}^{-2 x} \sin \left (3 x \right ) \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = {\mathrm e}^{-2 x} \sec \left (x \right ) \]

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

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {{\mathrm e}^{-3 x}}{x^{3}} \]

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

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-6 x y^{\prime }+10 y = 3 x^{4}+6 x^{3} \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0 \]

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0 \]

\[ {}9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \]

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+10 y = 0 \]

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

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3} \]

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

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

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

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-10 y = 0 \]

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

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

\[ {}x^{2} y^{\prime \prime }-2 y = 4 x -8 \]

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = -6 x^{3}+4 x^{2} \]

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 10 x^{2} \]

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3} \]

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

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

\[ {}\left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y = 0 \]

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

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

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

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

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