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

\[ {}x^{\prime \prime }+x^{\prime }+x = 12 \]

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

\[ {}x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (7 t \right ) \]

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

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

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

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

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

\[ {}x^{\prime \prime }+x^{\prime }+x = t^{3}+1-4 t \cos \left (t \right ) \]

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

\[ {}x^{\prime \prime }+7 x = t \,{\mathrm e}^{3 t} \]

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

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

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

\[ {}x^{\prime \prime }+x = 9 \,{\mathrm e}^{-t} \]

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

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

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

\[ {}x^{\prime \prime }-3 x^{\prime }-40 x = 2 \,{\mathrm e}^{-t} \]

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

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

\[ {}x^{\prime \prime }+\frac {x^{\prime }}{100}+4 x = \cos \left (2 t \right ) \]

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

\[ {}x^{\prime \prime }+3025 x = \cos \left (45 t \right ) \]

\[ {}x^{\prime \prime } = -\frac {x}{t^{2}} \]

\[ {}x^{\prime \prime } = \frac {4 x}{t^{2}} \]

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

\[ {}t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t} = 0 \]

\[ {}t^{2} x^{\prime \prime }-7 t x^{\prime }+16 x = 0 \]

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

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

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

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

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

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

\[ {}x^{\prime \prime }-x = \frac {1}{t} \]

\[ {}t^{2} x^{\prime \prime }-2 x = t^{3} \]

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

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

\[ {}x^{\prime \prime }+\frac {x^{\prime }}{t} = a \]

\[ {}t^{2} x^{\prime \prime }-3 t x^{\prime }+3 x = 4 t^{7} \]

\[ {}x^{\prime \prime }-x = \frac {{\mathrm e}^{t}}{1+{\mathrm e}^{t}} \]

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

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

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

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

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

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

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

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

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

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

\[ {}x^{\prime \prime }+9 x = \sin \left (3 t \right ) \]

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

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

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

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

\[ {}x^{\prime \prime }-x = \delta \left (t -5\right ) \]

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

\[ {}x^{\prime \prime }+4 x = \delta \left (t -2\right )-\delta \left (t -5\right ) \]

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

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

\[ {}x^{\prime \prime }+4 x = \frac {\left (t -5\right ) \operatorname {Heaviside}\left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right ) \]

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = 0 \]

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

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

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

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

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

\[ {}y^{\prime \prime }-y^{\prime }-12 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 2-12 x +6 \,{\mathrm e}^{x} \]

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]

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

\[ {}4 y^{\prime \prime }-12 y^{\prime }+5 y = 0 \]

\[ {}3 y^{\prime \prime }-14 y^{\prime }-5 y = 0 \]

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = 0 \]

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

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \]

\[ {}y^{\prime \prime }+6 y^{\prime }+25 y = 0 \]

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

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