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

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

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

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

\[ {}2 y^{\prime \prime }+5 y^{\prime }-3 y = \sin \left (x \right )-8 x \]

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{x}+\sin \left (4 x \right ) \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{\prime \prime }+\omega _{0}^{2} x = a \cos \left (\omega t \right ) \]

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

\[ {}f^{\prime \prime }+6 f^{\prime }+9 f = {\mathrm e}^{-t} \]

\[ {}f^{\prime \prime }+8 f^{\prime }+12 f = 12 \,{\mathrm e}^{-4 t} \]

\[ {}f^{\prime \prime }+8 f^{\prime }+12 f = 12 \,{\mathrm e}^{-4 t} \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y = {\mathrm e}^{-x^{2}} \sin \left (2 x \right ) \]

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 18 \,{\mathrm e}^{5 x} \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }+9 y = 5 \cos \left (2 x \right ) \]