\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 12 \operatorname {Heaviside}\relax (t )-12 \operatorname {Heaviside}\left (t -1\right ) \]

\[ {}y^{\prime \prime \prime \prime }-16 y = 32 \operatorname {Heaviside}\relax (t )-32 \operatorname {Heaviside}\left (-\pi +t \right ) \]

\[ {}t^{2} y^{\prime \prime }+3 y^{\prime } t +y = t^{7} \]

\[ {}t^{2} y^{\prime \prime }-6 y^{\prime } t +\sin \left (2 t \right ) y = \ln \relax (t ) \]

\[ {}y^{\prime \prime }+3 y^{\prime }+\frac {y}{t} = t \]

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

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

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

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{t} \]

\[ {}y^{\prime \prime }-3 y^{\prime }-7 y = 4 \]

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

\[ {}3 y^{\prime \prime }+5 y^{\prime }-2 y = 3 t^{2} \]

\[ {}y^{\prime \prime \prime } = 2 y^{\prime \prime }-4 y^{\prime }+\sin \relax (t ) \]

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

\[ {}\left [x^{\prime }\relax (t ) = \frac {5 x \relax (t )}{4}+\frac {3 y \relax (t )}{4}, y^{\prime }\relax (t ) = \frac {x \relax (t )}{2}-\frac {3 y \relax (t )}{2}\right ] \]

\[ {}[x^{\prime }\relax (t )-x \relax (t )+2 y \relax (t ) = 0, y^{\prime }\relax (t )+y \relax (t )-x \relax (t ) = 0] \]

\[ {}[x^{\prime }\relax (t )+5 x \relax (t )-2 y \relax (t ) = 0, y^{\prime }\relax (t )+2 x \relax (t )-y \relax (t ) = 0] \]

\[ {}[x^{\prime }\relax (t )-3 x \relax (t )+2 y \relax (t ) = 0, y^{\prime }\relax (t )-x \relax (t )+3 y \relax (t ) = 0] \]

\[ {}[x^{\prime }\relax (t )+x \relax (t )-z \relax (t ) = 0, y^{\prime }\relax (t )-y \relax (t )+x \relax (t ) = 0, z^{\prime }\relax (t )+x \relax (t )+2 y \relax (t )-3 z \relax (t ) = 0] \]

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

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

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

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

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

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

\[ {}[x^{\prime }\relax (t )-4 y^{\prime }\relax (t ) = 0, 2 x^{\prime }\relax (t )-3 y^{\prime }\relax (t ) = y \relax (t )+t] \]

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

\[ {}[x^{\prime }\relax (t ) = -4 x \relax (t )+9 y \relax (t )+12 \,{\mathrm e}^{-t}, y^{\prime }\relax (t ) = -5 x \relax (t )+2 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = -7 x \relax (t )+6 y \relax (t )+6 \,{\mathrm e}^{-t}, y^{\prime }\relax (t ) = -12 x \relax (t )+5 y \relax (t )+37] \]

\[ {}[x^{\prime }\relax (t ) = -7 x \relax (t )+10 y \relax (t )+18 \,{\mathrm e}^{t}, y^{\prime }\relax (t ) = -10 x \relax (t )+9 y \relax (t )+37] \]

\[ {}[x^{\prime }\relax (t ) = -14 x \relax (t )+39 y \relax (t )+78 \sinh \relax (t ), y^{\prime }\relax (t ) = -6 x \relax (t )+16 y \relax (t )+6 \cosh \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 2 x \relax (t )+4 y \relax (t )-2 z \relax (t )-2 \sinh \relax (t ), y^{\prime }\relax (t ) = 4 x \relax (t )+2 y \relax (t )-2 z \relax (t )+10 \cosh \relax (t ), z^{\prime }\relax (t ) = -x \relax (t )+3 y \relax (t )+z \relax (t )+5] \]

\[ {}[x^{\prime }\relax (t ) = 2 x \relax (t )+6 y \relax (t )-2 z \relax (t )+50 \,{\mathrm e}^{t}, y^{\prime }\relax (t ) = 6 x \relax (t )+2 y \relax (t )-2 z \relax (t )+21 \,{\mathrm e}^{-t}, z^{\prime }\relax (t ) = -x \relax (t )+6 y \relax (t )+z \relax (t )+9] \]

\[ {}[x^{\prime }\relax (t ) = -2 x \relax (t )-2 y \relax (t )+4 z \relax (t ), y^{\prime }\relax (t ) = -2 x \relax (t )+y \relax (t )+2 z \relax (t ), z^{\prime }\relax (t ) = -4 x \relax (t )-2 y \relax (t )+6 z \relax (t )+{\mathrm e}^{2 t}] \]

\[ {}[x^{\prime }\relax (t ) = 3 x \relax (t )-2 y \relax (t )+3 z \relax (t ), y^{\prime }\relax (t ) = x \relax (t )-y \relax (t )+2 z \relax (t )+2 \,{\mathrm e}^{-t}, z^{\prime }\relax (t ) = -2 x \relax (t )+2 y \relax (t )-2 z \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 7 x \relax (t )+y \relax (t )-1-6 \,{\mathrm e}^{t}, y^{\prime }\relax (t ) = -4 x \relax (t )+3 y \relax (t )+4 \,{\mathrm e}^{t}-3] \]

\[ {}[x^{\prime }\relax (t ) = 3 x \relax (t )-2 y \relax (t )+24 \sin \relax (t ), y^{\prime }\relax (t ) = 9 x \relax (t )-3 y \relax (t )+12 \cos \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 7 x \relax (t )-4 y \relax (t )+10 \,{\mathrm e}^{t}, y^{\prime }\relax (t ) = 3 x \relax (t )+14 y \relax (t )+6 \,{\mathrm e}^{2 t}] \]

\[ {}[x^{\prime }\relax (t ) = -7 x \relax (t )+4 y \relax (t )+6 \,{\mathrm e}^{3 t}, y^{\prime }\relax (t ) = -5 x \relax (t )+2 y \relax (t )+6 \,{\mathrm e}^{2 t}] \]

\[ {}[x^{\prime }\relax (t ) = -3 x \relax (t )-3 y \relax (t )+z \relax (t ), y^{\prime }\relax (t ) = 2 y \relax (t )+2 z \relax (t )+29 \,{\mathrm e}^{-t}, z^{\prime }\relax (t ) = 5 x \relax (t )+y \relax (t )+z \relax (t )+39 \,{\mathrm e}^{t}] \]

\[ {}[x^{\prime }\relax (t ) = 2 x \relax (t )+y \relax (t )-z \relax (t )+5 \sin \relax (t ), y^{\prime }\relax (t ) = y \relax (t )+z \relax (t )-10 \cos \relax (t ), z^{\prime }\relax (t ) = x \relax (t )+z \relax (t )+2] \]

\[ {}[x^{\prime }\relax (t ) = -3 x \relax (t )+3 y \relax (t )+z \relax (t )+5 \sin \left (2 t \right ), y^{\prime }\relax (t ) = x \relax (t )-5 y \relax (t )-3 z \relax (t )+5 \cos \left (2 t \right ), z^{\prime }\relax (t ) = -3 x \relax (t )+7 y \relax (t )+3 z \relax (t )+23 \,{\mathrm e}^{t}] \]

\[ {}[x^{\prime }\relax (t ) = -3 x \relax (t )+y \relax (t )-3 z \relax (t )+2 \,{\mathrm e}^{t}, y^{\prime }\relax (t ) = 4 x \relax (t )-y \relax (t )+2 z \relax (t )+4 \,{\mathrm e}^{t}, z^{\prime }\relax (t ) = 4 x \relax (t )-2 y \relax (t )+3 z \relax (t )+4 \,{\mathrm e}^{t}] \]

\[ {}[x^{\prime }\relax (t ) = x \relax (t )+5 y \relax (t )+10 \sinh \relax (t ), y^{\prime }\relax (t ) = 19 x \relax (t )-13 y \relax (t )+24 \sinh \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 9 x \relax (t )-3 y \relax (t )-6 t, y^{\prime }\relax (t ) = -x \relax (t )+11 y \relax (t )+10 t] \]

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

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

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

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

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

\[ {}y^{\prime \prime }+y = f \relax (x ) \]

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

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

\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (1-5 x \right ) y^{\prime }-4 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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