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Mathematica |
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = 1]
\]
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\[
{} [x^{\prime }\left (t \right ) = 0, y^{\prime }\left (t \right ) = -2 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )^{2}, y^{\prime }\left (t \right ) = {\mathrm e}^{t}]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 1]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+1, x_{2}^{\prime }\left (t \right ) = x_{2} \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+6 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 8 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+6 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+1]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+\sin \left (2 t \right )]
\]
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\[
{} \left [x_{1}^{\prime }\left (t \right ) = -2 t x_{1} \left (t \right )^{2}, x_{2}^{\prime }\left (t \right ) = \frac {x_{2} \left (t \right )+t}{t}\right ]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = {\mathrm e}^{t -x_{1} \left (t \right )}, x_{2}^{\prime }\left (t \right ) = 2 \,{\mathrm e}^{x_{1} \left (t \right )}]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = \frac {y \left (t \right )^{2}}{x \left (t \right )}\right ]
\]
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\[
{} \left [x_{1}^{\prime }\left (t \right ) = \frac {x_{1} \left (t \right )^{2}}{x_{2} \left (t \right )}, x_{2}^{\prime }\left (t \right ) = x_{2} \left (t \right )-x_{1} \left (t \right )\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = \frac {{\mathrm e}^{-x \left (t \right )}}{t}, y^{\prime }\left (t \right ) = \frac {x \left (t \right ) {\mathrm e}^{-y \left (t \right )}}{t}\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = \frac {y \left (t \right )+t}{x \left (t \right )+y \left (t \right )}, y^{\prime }\left (t \right ) = \frac {x \left (t \right )-t}{x \left (t \right )+y \left (t \right )}\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = \frac {t -y \left (t \right )}{-x \left (t \right )+y \left (t \right )}, y^{\prime }\left (t \right ) = \frac {x \left (t \right )-t}{-x \left (t \right )+y \left (t \right )}\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = \frac {y \left (t \right )+t}{x \left (t \right )+y \left (t \right )}, y^{\prime }\left (t \right ) = \frac {t +x \left (t \right )}{x \left (t \right )+y \left (t \right )}\right ]
\]
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\[
{} [x^{\prime }\left (t \right ) = -9 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right )+t, y^{\prime }\left (t \right ) = x \left (t \right )-t]
\]
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\[
{} [x^{\prime }\left (t \right )+3 x \left (t \right )+4 y \left (t \right ) = 0, y^{\prime }\left (t \right )+2 x \left (t \right )+5 y \left (t \right ) = 0]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+5 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-3 y \left (t \right )]
\]
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\[
{} [4 x^{\prime }\left (t \right )-y^{\prime }\left (t \right )+3 x \left (t \right ) = \sin \left (t \right ), x^{\prime }\left (t \right )+y \left (t \right ) = \cos \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = z \left (t \right ), z^{\prime }\left (t \right ) = -x \left (t \right )+z \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
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\[
{} [x^{\prime \prime }\left (t \right ) = y \left (t \right ), y^{\prime \prime }\left (t \right ) = x \left (t \right )]
\]
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\[
{} [x^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right ) = 0, x^{\prime }\left (t \right )+y^{\prime \prime }\left (t \right ) = 0]
\]
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\[
{} [x^{\prime \prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )]
\]
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\[
{} [x^{\prime \prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right ) x^{\prime }\left (t \right )+x \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right )^{2}, y^{\prime }\left (t \right ) = 2 x \left (t \right ) y \left (t \right )]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = -\frac {1}{y \left (t \right )}, y^{\prime }\left (t \right ) = \frac {1}{x \left (t \right )}\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = \frac {x \left (t \right )}{y \left (t \right )}, y^{\prime }\left (t \right ) = \frac {y \left (t \right )}{x \left (t \right )}\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = \frac {y \left (t \right )}{x \left (t \right )-y \left (t \right )}, y^{\prime }\left (t \right ) = \frac {x \left (t \right )}{x \left (t \right )-y \left (t \right )}\right ]
\]
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\[
{} [x^{\prime }\left (t \right ) = \sin \left (x \left (t \right )\right ) \cos \left (y \left (t \right )\right ), y^{\prime }\left (t \right ) = \cos \left (x \left (t \right )\right ) \sin \left (y \left (t \right )\right )]
\]
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\[
{} \left [{\mathrm e}^{t} x^{\prime }\left (t \right ) = \frac {1}{y \left (t \right )}, {\mathrm e}^{t} y^{\prime }\left (t \right ) = \frac {1}{x \left (t \right )}\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = \cos \left (x \left (t \right )\right )^{2} \cos \left (y \left (t \right )\right )^{2}+\sin \left (x \left (t \right )\right )^{2} \cos \left (y \left (t \right )\right )^{2}, y^{\prime }\left (t \right ) = -\frac {\sin \left (2 x \left (t \right )\right ) \sin \left (2 y \left (t \right )\right )}{2}\right ]
\]
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\[
{} [x^{\prime }\left (t \right ) = 8 y \left (t \right )-x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 4 y \left (t \right )-2 x \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right )+z \left (t \right )-x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-z \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+2 z \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = y \left (t \right )-2 z \left (t \right )-3 x \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right )+2 x \left (t \right )-y \left (t \right ) = -{\mathrm e}^{2 t}, y^{\prime }\left (t \right )+3 x \left (t \right )-2 y \left (t \right ) = 6 \,{\mathrm e}^{2 t}]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-\cos \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )-2 x \left (t \right )+\cos \left (t \right )+\sin \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right )+\tan \left (t \right )^{2}-1, y^{\prime }\left (t \right ) = \tan \left (t \right )-x \left (t \right )]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = -4 x \left (t \right )-2 y \left (t \right )+\frac {2}{{\mathrm e}^{t}-1}, y^{\prime }\left (t \right ) = 6 x \left (t \right )+3 y \left (t \right )-\frac {3}{{\mathrm e}^{t}-1}\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+\frac {1}{\cos \left (t \right )}\right ]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+1]
\]
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\[
{} [x^{\prime }\left (t \right ) = 3-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-2 t]
\]
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\[
{} [x^{\prime }\left (t \right ) = -y \left (t \right )+\sin \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+\cos \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+{\mathrm e}^{t}, y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-{\mathrm e}^{t}]
\]
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\[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-5 y \left (t \right )+4 t -1, y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )+t]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )+{\mathrm e}^{t}, y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+{\mathrm e}^{t}]
\]
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\[
{} [x^{\prime }\left (t \right )+y \left (t \right ) = t^{2}, -x \left (t \right )+y^{\prime }\left (t \right ) = t]
\]
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\[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+y \left (t \right ) = {\mathrm e}^{-t}, 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 y \left (t \right ) = \sin \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )-2 z \left (t \right )+2-t, y^{\prime }\left (t \right ) = -x \left (t \right )+1, z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-z \left (t \right )+1-t]
\]
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\[
{} [x^{\prime }\left (t \right )+x \left (t \right )+2 y \left (t \right ) = 2 \,{\mathrm e}^{-t}, y^{\prime }\left (t \right )+y \left (t \right )+z \left (t \right ) = 1, z^{\prime }\left (t \right )+z \left (t \right ) = 1]
\]
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\[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 6 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+3 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-4 y \left (t \right )+1, y^{\prime }\left (t \right ) = -x \left (t \right )+5 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )+{\mathrm e}^{t}, y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )-{\mathrm e}^{t}]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+4 y \left (t \right )+\cos \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )+\sin \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+4]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )+\sin \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )-\cos \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -2 t x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )+4, y^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )-3]
\]
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\[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+t y \left (t \right ), y^{\prime }\left (t \right ) = t x \left (t \right )-y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+4, y^{\prime }\left (t \right ) = -2 x \left (t \right )+\sin \left (t \right ) y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 \sin \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-4 y \left (t \right )+2 t, y^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right )-3]
\]
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\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )+1, y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-3]
\]
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\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )-4 y \left (t \right )-4, y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )-6]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = -\frac {x \left (t \right )}{4}-\frac {3 y \left (t \right )}{4}+8, y^{\prime }\left (t \right ) = \frac {x \left (t \right )}{2}+y \left (t \right )-\frac {23}{2}\right ]
\]
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\[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )-11, y^{\prime }\left (t \right ) = -5 x \left (t \right )+4 y \left (t \right )-35]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-3, y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )+1]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -5 x \left (t \right )+4 y \left (t \right )-35, y^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )-11]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )-6 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left [x^{\prime }\left (t \right ) = \frac {5 x \left (t \right )}{4}+\frac {3 y \left (t \right )}{4}, y^{\prime }\left (t \right ) = \frac {3 x \left (t \right )}{4}+\frac {5 y \left (t \right )}{4}\right ]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left [x^{\prime }\left (t \right ) = -\frac {3 x \left (t \right )}{4}-\frac {7 y \left (t \right )}{4}, y^{\prime }\left (t \right ) = \frac {x \left (t \right )}{4}+\frac {5 y \left (t \right )}{4}\right ]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left [x^{\prime }\left (t \right ) = -\frac {x \left (t \right )}{4}-\frac {3 y \left (t \right )}{4}, y^{\prime }\left (t \right ) = \frac {x \left (t \right )}{2}+y \left (t \right )\right ]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -5 x \left (t \right )+4 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+6 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -5 x \left (t \right )+4 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|