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ODE |
Mathematica |
Maple |
Sympy |
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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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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+2 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )-3 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )+5 y \left (t \right )+4 \,{\mathrm e}^{t} \cos \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-2 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )+{\mathrm e}^{t}, y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+{\mathrm e}^{t}]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-5 y \left (t \right )+\sin \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )+\tan \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right )+\textit {f\_1} \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+f_{2} \left (t \right )]
\]
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\[
{} y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y = 0
\]
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\[
{} y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }-8 y = 0
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 0
\]
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\[
{} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y = 0
\]
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\[
{} y^{\prime \prime \prime \prime }-y = 0
\]
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\[
{} y^{\left (5\right )}-2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime } = 0
\]
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\[
{} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }+2 y^{\prime }-2 y = 0
\]
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\[
{} y^{\prime \prime \prime }+y^{\prime } = \tan \left (t \right )
\]
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\[
{} y^{\prime \prime \prime \prime }-y = g \left (t \right )
\]
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\[
{} y^{\prime \prime \prime \prime }+y = g \left (t \right )
\]
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\[
{} y^{\prime \prime \prime }+y^{\prime } = 2 t^{2}+4 \sin \left (t \right )
\]
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\[
{} y^{\prime \prime \prime }-4 y^{\prime } = t +\cos \left (t \right )+2 \,{\mathrm e}^{-2 t}
\]
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\[
{} y^{\prime \prime \prime \prime }-y = t +\sin \left (t \right )
\]
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\[
{} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = t^{2} \sin \left (t \right )
\]
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\[
{} y^{\prime \prime \prime \prime }+y^{\prime \prime } = t^{2}
\]
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\[
{} y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y = t +{\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y = t^{3} {\mathrm e}^{-t}
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+2 x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 7 x_{1} \left (t \right )-x_{2} \left (t \right )+6 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -10 x_{1} \left (t \right )+4 x_{2} \left (t \right )-12 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = -7 x_{1} \left (t \right )+6 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+2 x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )+3 x_{3} \left (t \right )+6 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+6 x_{2} \left (t \right )+9 x_{3} \left (t \right )+18 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+10 x_{2} \left (t \right )+15 x_{3} \left (t \right )+30 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 7 x_{1} \left (t \right )+14 x_{2} \left (t \right )+21 x_{3} \left (t \right )+42 x_{4} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+2 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+3 x_{2} \left (t \right )-x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+10 x_{2} \left (t \right )+2 x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-3 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{2} \left (t \right )-2 x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )-3 x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-3 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-3 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -3 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 3 x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = -x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-3 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -x_{3} \left (t \right )+2 x_{4} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )-4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 10 x_{1} \left (t \right )+9 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )-3 x_{2} \left (t \right )+x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+4 x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 2 x_{3} \left (t \right )+3 x_{4} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right )+{\mathrm e}^{t} \cos \left (2 t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+{\mathrm e}^{c t}, x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+5 x_{2} \left (t \right )+4 \,{\mathrm e}^{t} \cos \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-4 x_{2} \left (t \right )+{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+{\mathrm e}^{t}]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-5 x_{2} \left (t \right )+\sin \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )+\tan \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right )+f_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+f_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{3} \left (t \right )+{\mathrm e}^{2 t}, x_{2}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{2} \left (t \right )+3 x_{3} \left (t \right )+{\mathrm e}^{2 t}]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-x_{2} \left (t \right )-2 x_{3} \left (t \right )+{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )+{\mathrm e}^{3 t}, x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right )+{\mathrm e}^{3 t}]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )-t^{2}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right )+2 t]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right )+2 x_{3} \left (t \right )+\sin \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right )]
\]
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✓ |
✓ |
✓ |
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right )+{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+4 x_{3} \left (t \right )-{\mathrm e}^{t}]
\]
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✓ |
✓ |
✓ |
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\[
{} [x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-x_{2} \left (t \right )+1, x_{2}^{\prime }\left (t \right ) = -4 x_{2} \left (t \right )-x_{3} \left (t \right )+t, x_{3}^{\prime }\left (t \right ) = 5 x_{2} \left (t \right )+{\mathrm e}^{t}]
\]
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✓ |
✓ |
✓ |
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )+{\mathrm e}^{2 t}, x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+3 x_{2} \left (t \right )-4 x_{3} \left (t \right )+2 \,{\mathrm e}^{2 t}, x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )-4 x_{3} \left (t \right )+{\mathrm e}^{2 t}]
\]
|
✓ |
✓ |
✓ |
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right )+{\mathrm e}^{3 t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right )+x_{3} \left (t \right )-{\mathrm e}^{3 t}, x_{3}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )-{\mathrm e}^{3 t}]
\]
|
✓ |
✓ |
✓ |
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\[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 x_{3} \left (t \right )+2 \,{\mathrm e}^{8 t}, x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{3} \left (t \right )+{\mathrm e}^{8 t}, x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+2 x_{2} \left (t \right )+3 x_{3} \left (t \right )+2 \,{\mathrm e}^{8 t}]
\]
|
✓ |
✓ |
✓ |
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+2 x_{2} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-3 x_{2} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
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\[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right )+t, x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-2 x_{2} \left (t \right )+3 \,{\mathrm e}^{t}]
\]
|
✓ |
✓ |
✓ |
|
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+2 \,{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )-{\mathrm e}^{t}]
\]
|
✓ |
✓ |
✓ |
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\[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-4 x_{2} \left (t \right )+{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+{\mathrm e}^{t}]
\]
|
✓ |
✓ |
✓ |
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\[
{} [x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-5 x_{2} \left (t \right )+\sin \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )+\tan \left (t \right )]
\]
|
✓ |
✓ |
✓ |
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\[
{} [x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+5 x_{2} \left (t \right )+4 \,{\mathrm e}^{t} \cos \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right )+f_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+f_{2} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
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\[
{} [x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-2 x_{2} \left (t \right )+\delta \left (t -\pi \right )]
\]
|
✓ |
✓ |
✓ |
|
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\[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right )+1-\operatorname {Heaviside}\left (t -\pi \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+4 x_{3} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
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\[
{} [x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{3} \left (t \right )+{\mathrm e}^{2 t}, x_{2}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{3} \left (t \right )+{\mathrm e}^{2 t}]
\]
|
✓ |
✓ |
✓ |
|
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\[
{} [x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-x_{2} \left (t \right )+2 x_{3} \left (t \right )+{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\]
|
✓ |
✓ |
✗ |
|
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right )+{\mathrm e}^{t} \cos \left (2 t \right )]
\]
|
✓ |
✓ |
✓ |
|
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\[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 2 x_{3} \left (t \right )+3 x_{4} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right )^{2}-2 x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )-2 y \left (t \right )^{2}-3 x \left (t \right ) y \left (t \right )]
\]
|
✗ |
✗ |
✗ |
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\[
{} [x^{\prime }\left (t \right ) = -b x \left (t \right ) y \left (t \right )+m, y^{\prime }\left (t \right ) = b x \left (t \right ) y \left (t \right )-g y \left (t \right )]
\]
|
✗ |
✗ |
✗ |
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\[
{} [x^{\prime }\left (t \right ) = a x \left (t \right )-b x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = -c y \left (t \right )+d x \left (t \right ) y \left (t \right ), z^{\prime }\left (t \right ) = z \left (t \right )+x \left (t \right )^{2}+y \left (t \right )^{2}]
\]
|
✓ |
✓ |
✗ |
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\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )-x \left (t \right ) y \left (t \right )^{2}, y^{\prime }\left (t \right ) = -y \left (t \right )-y \left (t \right ) x \left (t \right )^{2}, z^{\prime }\left (t \right ) = 1-z \left (t \right )+x \left (t \right )^{2}]
\]
|
✓ |
✓ |
✗ |
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right ) y \left (t \right )^{2}-x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right ) \sin \left (\pi y \left (t \right )\right )]
\]
|
✓ |
✓ |
✗ |
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\[
{} [x^{\prime }\left (t \right ) = \cos \left (y \left (t \right )\right ), y^{\prime }\left (t \right ) = \sin \left (x \left (t \right )\right )-1]
\]
|
✓ |
✓ |
✗ |
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\[
{} [x^{\prime }\left (t \right ) = -1-y \left (t \right )-{\mathrm e}^{x \left (t \right )}, y^{\prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right ) \left ({\mathrm e}^{x \left (t \right )}-1\right ), z^{\prime }\left (t \right ) = x \left (t \right )+\sin \left (z \left (t \right )\right )]
\]
|
✗ |
✗ |
✗ |
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )^{2}, y^{\prime }\left (t \right ) = x \left (t \right )^{2}-y \left (t \right ), z^{\prime }\left (t \right ) = {\mathrm e}^{z \left (t \right )}-x \left (t \right )]
\]
|
✓ |
✓ |
✗ |
|
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+z \left (t \right )-2 \,{\mathrm e}^{-t}, y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )-z \left (t \right )-2 \,{\mathrm e}^{-t}, z^{\prime }\left (t \right ) = -3 x \left (t \right )+2 y \left (t \right )+4 z \left (t \right )+3 \,{\mathrm e}^{-t}]
\]
|
✓ |
✓ |
✓ |
|
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
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\[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|