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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-14] \]

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

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

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

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

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

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

\[ {}[x^{\prime }\left (t \right ) = 5 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )] \]

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

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

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

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

\[ {}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )+3 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = -5 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-10 y \left (t \right )] \]

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

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

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

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

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

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

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

\[ {}[x^{\prime }\left (t \right ) = -5 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{-t}, y^{\prime }\left (t \right ) = 2 x \left (t \right )-10 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+\cos \left (t w \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )+3, y^{\prime }\left (t \right ) = 7 x \left (t \right )+5 y \left (t \right )+2 t] \]

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+7 y \left (t \right )] \]

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-4 y^{\prime }+8 y = 0 \]

\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0 \]

\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y = 0 \]

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

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

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

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

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

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

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

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

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