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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {2 \,{\mathrm e}^{-3 x}}{x^{2}+1} \]

\[ {}y^{\prime \prime }-4 y = \frac {8}{{\mathrm e}^{2 x}+1} \]

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

\[ {}y^{\prime \prime }+9 y = \frac {36}{4-\cos \left (3 x \right )^{2}} \]

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = \frac {2 \,{\mathrm e}^{5 x}}{x^{2}+4} \]

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 4 \,{\mathrm e}^{3 x} \sec \left (2 x \right )^{2} \]

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

\[ {}y^{\prime \prime }+y = \csc \left (x \right )+2 x^{2}+5 x +1 \]

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

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

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

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

\[ {}y^{\prime \prime }+2 y^{\prime }+17 y = \frac {64 \,{\mathrm e}^{-x}}{3+\sin \left (4 x \right )^{2}} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {4 \,{\mathrm e}^{-2 x}}{x^{2}+1}+2 x^{2}-1 \]

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 15 \,{\mathrm e}^{-2 x} \ln \left (x \right )+25 \cos \left (x \right ) \]

\[ {}y^{\prime \prime }-9 y = F \left (x \right ) \]

\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = F \left (x \right ) \]

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y = 8 x^{2} {\mathrm e}^{2 x} \]

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

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 15 \,{\mathrm e}^{3 x} \sqrt {x} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-y^{\prime }-12 y = 36 \]

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

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

\[ {}y^{\prime \prime }-2 y^{\prime } = 30 \,{\mathrm e}^{-3 t} \]

\[ {}y^{\prime \prime }-y = 12 \,{\mathrm e}^{2 t} \]

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

\[ {}y^{\prime \prime }-y^{\prime }-6 y = -6 \,{\mathrm e}^{t}+12 \]

\[ {}y^{\prime \prime }-y = 6 \cos \left (t \right ) \]

\[ {}y^{\prime \prime }-9 y = 13 \sin \left (2 t \right ) \]

\[ {}y^{\prime \prime }-y = 8 \sin \left (t \right )-6 \cos \left (t \right ) \]

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 10 \cos \left (t \right ) \]

\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right ) \]

\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right ) \]

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

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

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

\[ {}y^{\prime \prime }+9 y = 7 \sin \left (4 t \right )+14 \cos \left (4 t \right ) \]

\[ {}y^{\prime \prime }-y = \operatorname {Heaviside}\left (-1+t \right ) \]

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 1-3 \operatorname {Heaviside}\left (t -2\right ) \]

\[ {}y^{\prime \prime }-4 y = \operatorname {Heaviside}\left (-1+t \right )-\operatorname {Heaviside}\left (t -2\right ) \]

\[ {}y^{\prime \prime }+y = t -\operatorname {Heaviside}\left (-1+t \right ) \left (-1+t \right ) \]

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = -10 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \cos \left (t +\frac {\pi }{4}\right ) \]

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 30 \operatorname {Heaviside}\left (-1+t \right ) {\mathrm e}^{1-t} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 5 \operatorname {Heaviside}\left (t -3\right ) \]

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 2 \sin \left (t \right )+\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (1+\cos \left (t \right )\right ) \]

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

\[ {}y^{\prime \prime }-4 y = \delta \left (t -3\right ) \]

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -\frac {\pi }{2}\right ) \]

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right ) \]

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

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right ) \]

\[ {}y^{\prime \prime }+9 y = 15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right ) \]

\[ {}y^{\prime \prime }+16 y = 4 \cos \left (3 t \right )+\delta \left (t -\frac {\pi }{3}\right ) \]