\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2} \]

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

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

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

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

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

\[ {}y^{\prime \prime \prime }+4 y^{\prime \prime }-5 y^{\prime } = x^{2} {\mathrm e}^{-x} \]

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

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

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

\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+9 y^{\prime \prime } = \sin \left (3 x \right )+x \,{\mathrm e}^{x} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+16 y = 0 \]

\[ {}4 x^{2} y^{\prime \prime }-16 x y^{\prime }+25 y = 0 \]

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

\[ {}2 x^{2} y^{\prime \prime }-3 x y^{\prime }-18 y = \ln \left (x \right ) \]

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

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

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

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

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

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

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

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

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

\[ {}x^{4} y^{\prime \prime \prime \prime }+7 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }-6 x y^{\prime }-6 y = \cos \left (\ln \left (x \right )\right ) \]

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

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

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

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

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

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

\[ {}[5 y^{\prime }\left (t \right )-3 x^{\prime }\left (t \right )-5 y \left (t \right ) = 5 t, 3 x^{\prime }\left (t \right )-5 y^{\prime }\left (t \right )-2 x \left (t \right ) = 0] \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{\prime \prime }+t x^{\prime } = t^{3} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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