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

\[ {}y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 4 \,{\mathrm e}^{2 x}-21 \,{\mathrm e}^{-3 x} \]

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 6 \sin \left (2 x \right )+7 \cos \left (2 x \right ) \]

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 10 \sin \left (4 x \right ) \]

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

\[ {}y^{\prime \prime }-3 y^{\prime }-4 y = 16 x -12 \,{\mathrm e}^{2 x} \]

\[ {}y^{\prime \prime }+6 y^{\prime }+5 y = 2 \,{\mathrm e}^{x}+10 \,{\mathrm e}^{5 x} \]

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

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 10 \,{\mathrm e}^{2 x}-18 \,{\mathrm e}^{3 x}-6 x -11 \]

\[ {}y^{\prime \prime }+y^{\prime }-2 y = 6 \,{\mathrm e}^{-2 x}+3 \,{\mathrm e}^{x}-4 x^{2} \]

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

\[ {}y^{\prime \prime }+4 y = 12 x^{2}-16 x \cos \left (2 x \right ) \]

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4 \]

\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 16 x +20 \,{\mathrm e}^{x} \]

\[ {}y^{\prime \prime }-8 y^{\prime }+15 y = 9 \,{\mathrm e}^{2 x} x \]

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = 4 x \,{\mathrm e}^{-3 x} \]

\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = 8 \,{\mathrm e}^{-2 x} \]

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 27 \,{\mathrm e}^{-6 x} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 18 \,{\mathrm e}^{-2 x} \]

\[ {}y^{\prime \prime }-10 y^{\prime }+29 y = 8 \,{\mathrm e}^{5 x} \]

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 8 \sin \left (3 x \right ) \]

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 8 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x} \]

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

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

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

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

\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = x^{3}+x +{\mathrm e}^{-2 x} \]

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

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = {\mathrm e}^{-2 x} \left (\cos \left (x \right )+1\right ) \]

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = x^{4} {\mathrm e}^{x}+x^{3} {\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \]

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

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

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

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

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

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

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

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

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