\[ {}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -5 x_{1} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{2} \left (t \right )] \]

\[ {}\left [x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-\frac {5 x_{2} \left (t \right )}{2}, x_{2}^{\prime }\left (t \right ) = \frac {9 x_{1} \left (t \right )}{5}-x_{2} \left (t \right )\right ] \]

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

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

\[ {}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-x_{2} \left (t \right )-1, x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+5] \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}t^{2} \left (t +3\right ) y^{\prime \prime \prime }-3 t \left (2+t \right ) y^{\prime \prime }+6 \left (t +1\right ) y^{\prime }-6 y = 0 \]

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

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

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

\[ {}y^{\left (6\right )}+y = 0 \]

\[ {}y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y = 0 \]

\[ {}y^{\left (6\right )}-y^{\prime \prime } = 0 \]

\[ {}y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0 \]

\[ {}y^{\left (8\right )}+8 y^{\prime \prime \prime \prime }+16 y = 0 \]

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

\[ {}y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime }+2 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+6 y^{\prime \prime }+30 y^{\prime }-36 y = 0 \]

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

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

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

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

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

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = 0 \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <3 \pi \\ 0 & 3 \pi \le t <\infty \end {array}\right . \]

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

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

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & \operatorname {otherwise} \end {array}\right . \]

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

\[ {}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \operatorname {otherwise} \end {array}\right . \]

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

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

\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = k \left (\operatorname {Heaviside}\left (t -\frac {3}{2}\right )-\operatorname {Heaviside}\left (t -\frac {5}{2}\right )\right ) \]

\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\operatorname {Heaviside}\left (t -\frac {3}{2}\right )}{2}-\frac {\operatorname {Heaviside}\left (t -\frac {5}{2}\right )}{2} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = \cos \left (x \right )-y \tan \left (x \right ) \]

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

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

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

\[ {}y^{\prime } = a y^{\frac {-1+a}{a}} \]

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

\[ {}y^{\prime } = -1-\frac {x}{2}+\frac {\sqrt {x^{2}+4 x +4 y}}{2} \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime }+3 y = 1 \]

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

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