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

\[ {}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 10 x^{3}-2 x +5 \]

\[ {}y^{\prime }-y = 1 \]

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

\[ {}y^{\prime }+6 y = {\mathrm e}^{4 t} \]

\[ {}y^{\prime }-y = 2 \cos \left (5 t \right ) \]

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

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

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

\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{t} \]

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

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

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

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \]

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

\[ {}y^{\prime }-y = 1+t \,{\mathrm e}^{t} \]

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

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

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = t \]

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

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 0 \]

\[ {}2 y^{\prime \prime }+20 y^{\prime }+51 y = 0 \]

\[ {}y^{\prime \prime }-y = {\mathrm e}^{t} \cos \relax (t ) \]

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = t +1 \]

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

\[ {}y^{\prime \prime }+8 y^{\prime }+20 y = 0 \]

\[ {}y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 5 & 1\le t \end {array}\right . \]

\[ {}y^{\prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \]

\[ {}y^{\prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \]

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \]

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

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = \theta \left (t -1\right ) \]

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \]

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 1-\theta \left (t -2\right )-\theta \left (t -4\right )+\theta \left (t -6\right ) \]

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

\[ {}y^{\prime }-y = t \,{\mathrm e}^{t} \sin \relax (t ) \]

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

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

\[ {}y^{\prime \prime }+16 y = \left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ \sin \relax (t ) & \frac {\pi }{2}\le t \end {array}\right . \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }+16 y = \delta \left (-2 \pi +t \right ) \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = \delta \left (-\pi +t \right )+\delta \left (-3 \pi +t \right ) \]

\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = {\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (t -4\right ) \]

\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 0 \]

\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = \delta \relax (t ) \]

\[ {}[x^{\prime }\relax (t ) = 3 x \relax (t )-5 y \relax (t ), y^{\prime }\relax (t ) = 4 x \relax (t )+8 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 4 x \relax (t )-7 y \relax (t ), y^{\prime }\relax (t ) = 5 x \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = -3 x \relax (t )+4 y \relax (t )-9 z \relax (t ), y^{\prime }\relax (t ) = 6 x \relax (t )-y \relax (t ), z^{\prime }\relax (t ) = 10 x \relax (t )+4 y \relax (t )+3 z \relax (t )] \]

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

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

\[ {}[x^{\prime }\relax (t ) = -3 x \relax (t )+4 y \relax (t )+{\mathrm e}^{-t} \sin \left (2 t \right ), y^{\prime }\relax (t ) = 5 x \relax (t )+9 z \relax (t )+4 \,{\mathrm e}^{-t} \cos \left (2 t \right ), z^{\prime }\relax (t ) = y \relax (t )+6 z \relax (t )-{\mathrm e}^{-t}] \]

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

\[ {}[x^{\prime }\relax (t ) = 7 x \relax (t )+5 y \relax (t )-9 z \relax (t )-8 \,{\mathrm e}^{-2 t}, y^{\prime }\relax (t ) = 4 x \relax (t )+y \relax (t )+z \relax (t )+2 \,{\mathrm e}^{5 t}, z^{\prime }\relax (t ) = -2 y \relax (t )+3 z \relax (t )+{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-2 t}] \]

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

\[ {}[x^{\prime }\relax (t ) = 3 x \relax (t )-7 y \relax (t )+4 \sin \relax (t )+\left (t -4\right ) {\mathrm e}^{4 t}, y^{\prime }\relax (t ) = x \relax (t )+y \relax (t )+8 \sin \relax (t )+\left (2 t +1\right ) {\mathrm e}^{4 t}] \]

\[ {}[x^{\prime }\relax (t ) = 3 x \relax (t )-4 y \relax (t ), y^{\prime }\relax (t ) = 4 x \relax (t )-7 y \relax (t )] \]

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

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

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

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

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

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

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

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

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

\[ {}[x^{\prime }\relax (t ) = 10 x \relax (t )-5 y \relax (t ), y^{\prime }\relax (t ) = 8 x \relax (t )-12 y \relax (t )] \]

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

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

\[ {}[x^{\prime }\relax (t ) = 2 x \relax (t )-7 y \relax (t ), y^{\prime }\relax (t ) = 5 x \relax (t )+10 y \relax (t )+4 z \relax (t ), z^{\prime }\relax (t ) = 5 y \relax (t )+2 z \relax (t )] \]

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

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

\[ {}\left [x^{\prime }\relax (t ) = -x \relax (t )-y \relax (t ), y^{\prime }\relax (t ) = \frac {3 x \relax (t )}{4}-\frac {3 y \relax (t )}{2}+3 z \relax (t ), z^{\prime }\relax (t ) = \frac {x \relax (t )}{8}+\frac {y \relax (t )}{4}-\frac {z \relax (t )}{2}\right ] \]

\[ {}\left [x^{\prime }\relax (t ) = -x \relax (t )-y \relax (t ), y^{\prime }\relax (t ) = \frac {3 x \relax (t )}{4}-\frac {3 y \relax (t )}{2}+3 z \relax (t ), z^{\prime }\relax (t ) = \frac {x \relax (t )}{8}+\frac {y \relax (t )}{4}-\frac {z \relax (t )}{2}\right ] \]

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

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

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

\[ {}\left [x^{\prime }\relax (t ) = \frac {9 x \relax (t )}{10}+\frac {21 y \relax (t )}{10}+\frac {16 z \relax (t )}{5}, y^{\prime }\relax (t ) = \frac {7 x \relax (t )}{10}+\frac {13 y \relax (t )}{2}+\frac {21 z \relax (t )}{5}, z^{\prime }\relax (t ) = \frac {11 x \relax (t )}{10}+\frac {17 y \relax (t )}{10}+\frac {17 z \relax (t )}{5}\right ] \]

\[ {}\left [x_{1}^{\prime }\relax (t ) = x_{1} \relax (t )+2 x_{3} \relax (t )-\frac {9 x_{4} \relax (t )}{5}, x_{2}^{\prime }\relax (t ) = \frac {51 x_{2} \relax (t )}{10}-x_{4} \relax (t )+3 x_{5} \relax (t ), x_{3}^{\prime }\relax (t ) = x_{1} \relax (t )+2 x_{2} \relax (t )-3 x_{3} \relax (t ), x_{4}^{\prime }\relax (t ) = x_{2} \relax (t )-\frac {31 x_{3} \relax (t )}{10}+4 x_{4} \relax (t ), x_{5}^{\prime }\relax (t ) = -\frac {14 x_{1} \relax (t )}{5}+\frac {3 x_{4} \relax (t )}{2}-x_{5} \relax (t )\right ] \]

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

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

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

\[ {}[x^{\prime }\relax (t ) = 12 x \relax (t )-9 y \relax (t ), y^{\prime }\relax (t ) = 4 x \relax (t )] \]

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

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

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

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

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

\[ {}[x^{\prime }\relax (t ) = 4 x \relax (t )+y \relax (t ), y^{\prime }\relax (t ) = 4 y \relax (t )+z \relax (t ), z^{\prime }\relax (t ) = 4 z \relax (t )] \]