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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-25 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0 \]

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-36 y = 0 \]

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

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }-8 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+\omega ^{2} y = \frac {F_{0} \cos \left (\omega t \right )}{m} \]

\[ {}y^{\prime \prime }-4 y^{\prime }+6 y = 7 \,{\mathrm e}^{2 x} \]

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

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

\[ {}y^{\prime \prime }-16 y = 20 \cos \left (4 x \right ) \]

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 50 \sin \left (3 x \right ) \]

\[ {}y^{\prime \prime }-y = 10 \,{\mathrm e}^{2 x} \cos \left (x \right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 169 \sin \left (3 x \right ) \]

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 40 \sin \left (x \right )^{2} \]

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

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

\[ {}y^{\prime \prime }-4 y = 100 \,{\mathrm e}^{x} \sin \left (x \right ) x \]

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

\[ {}y^{\prime \prime }-2 y^{\prime }+10 y = 24 \,{\mathrm e}^{x} \cos \left (3 x \right ) \]

\[ {}y^{\prime \prime }+16 y = 34 \,{\mathrm e}^{x}+16 \cos \left (4 x \right )-8 \sin \left (4 x \right ) \]

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 4 \,{\mathrm e}^{3 x} \ln \left (x \right ) \]

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

\[ {}y^{\prime \prime }+9 y = 18 \sec \left (3 x \right )^{3} \]