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

\[ {}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )] \]

\[ {}[t x^{\prime }\left (t \right )+2 x \left (t \right ) = 15 y \left (t \right ), t y^{\prime }\left (t \right ) = x \left (t \right )] \]

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

\[ {}[x^{\prime }\left (t \right ) = 5 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )+y \left (t \right )] \]

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

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

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

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

\[ {}[x^{\prime }\left (t \right ) = -2 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-13 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )] \]

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

\[ {}[x^{\prime }\left (t \right ) = 8 x \left (t \right )+2 y \left (t \right )-17, y^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )-13] \]

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

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

\[ {}[x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+24 t] \]

\[ {}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-13 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+19 \cos \left (4 t \right )-13 \sin \left (4 t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 4 x \left (t \right )+3 y \left (t \right )+5 \operatorname {Heaviside}\left (t -2\right ), y^{\prime }\left (t \right ) = x \left (t \right )+6 y \left (t \right )+17 \operatorname {Heaviside}\left (t -2\right )] \]

\[ {}[x^{\prime }\left (t \right ) = 5 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )+y \left (t \right )] \]

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

\[ {}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-5 y \left (t \right )+4, y^{\prime }\left (t \right ) = 3 x \left (t \right )-7 y \left (t \right )+5] \]

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

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right ) y \left (t \right )-6 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )-5] \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+9 y^{\prime } = 0 \]

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

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

\[ {}y^{\prime \prime }-12 y^{\prime }+40 y = 0 \]

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

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

\[ {}x^{2} y^{\prime \prime }-12 x y^{\prime }+42 y = 0 \]

\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+5 y = 0 \]

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

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

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

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

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

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

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

\[ {}y^{\prime } = \frac {x}{\sqrt {x^{2}-16}} \]

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

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

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

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

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

\[ {}y^{\prime } = \frac {\sqrt {x^{2}-16}}{x} \]

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

\[ {}y^{\prime } = \frac {1}{x^{2}-16} \]

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

\[ {}y^{\prime } = \sin \left (x \right )^{3} \tan \left (x \right ) \]

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

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

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

\[ {}y^{\prime \prime }+9 y^{\prime } = 0 \]

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

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

\[ {}t^{2} y^{\prime \prime }-12 t y^{\prime }+42 y = 0 \]

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y = 0 \]

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

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

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

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

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

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

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

\[ {}16 y^{\prime \prime }+24 y^{\prime }+153 y = 0 \]

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

\[ {}4 x \left (y^{2}+x^{2}\right )-5 y+4 y \left (x^{2}+y^{2}-5 x \right ) y^{\prime } = 0 \]

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

\[ {}y^{\prime \prime \prime \prime }+\frac {25 y^{\prime \prime }}{2}-5 y^{\prime }+\frac {629 y}{16} = 0 \]

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

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

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

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

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

\[ {}y^{\prime \prime }-6 y^{\prime }+45 y = 0 \]

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-16 y = 0 \]

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

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

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = 2 \]

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

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

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

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

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

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

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