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

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

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

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

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{-2 x} \sec \left (x \right )^{2} \left (1+2 \tan \left (x \right )\right ) \]

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

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

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

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

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

\[ {}\left (1+2 x \right )^{2} y^{\prime \prime }-2 \left (1+2 x \right ) y^{\prime }-12 y = 6 x \]

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

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

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

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

\[ {}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-10 y = 0 \]

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

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

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

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

\[ {}x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y = \frac {1+x}{x} \]

\[ {}x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y = \frac {1}{x^{3}} \]

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

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

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

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (9 x^{2}+6\right ) y = 0 \]

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

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

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

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

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

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

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

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

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

\[ {}\left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 x y^{\prime }-4 y = 8 \]

\[ {}\left (2 x^{3}-1\right ) y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+6 x y^{\prime } = 0 \]

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

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

\[ {}\left (1+2 y+3 y^{2}\right ) y^{\prime \prime \prime }+6 y^{\prime } \left (y^{\prime \prime }+{y^{\prime }}^{2}+3 y y^{\prime \prime }\right ) = x \]

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

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

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

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

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

\[ {}[x^{\prime }\left (t \right )+x \left (t \right )+2 y^{\prime }\left (t \right )+7 y \left (t \right ) = {\mathrm e}^{t}+2, -2 x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right ) = {\mathrm e}^{t}-1] \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}z^{\prime \prime }+t z^{\prime }+\left (t^{2}-\frac {1}{9}\right ) z = 0 \]

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

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

\[ {}x^{3} \left (1+x \right ) y^{\prime \prime \prime }-\left (2+4 x \right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-\left (4+12 x \right ) y = 0 \]

\[ {}x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-\left (12 x^{2}+4\right ) y = 0 \]

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

\[ {}\left (1-x \right ) x^{2} y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y = 0 \]

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

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

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

\[ {}\left (x -1\right ) \left (-2+x \right ) y^{\prime \prime }+\left (4 x -6\right ) y^{\prime }+2 y = 0 \]

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

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

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{3} y^{\prime \prime }+y = \frac {1}{x^{4}} \]