| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0
\]
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| \[
{} y^{\prime \prime } \cos \left (x \right )+y = 0
\]
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| \[
{} y^{\prime \prime }+x y^{\prime }+2 y = 0
\]
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| \[
{} \left (x +2\right ) y^{\prime \prime }+3 y = 0
\]
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| \[
{} \left (1-2 \sin \left (x \right )\right ) y^{\prime \prime }+x y = 0
\]
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| \[
{} y+x y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} x y^{\prime \prime }+\left (1-\cos \left (x \right )\right ) y^{\prime }+x^{2} y = 0
\]
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| \[
{} \left ({\mathrm e}^{x}-1-x \right ) y^{\prime \prime }+x y = 0
\]
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| \[
{} y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 10 x^{3}-2 x +5
\]
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| \[
{} -y+y^{\prime } = 1
\]
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| \[
{} y+2 y^{\prime } = 0
\]
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| \[
{} y^{\prime }+6 y = {\mathrm e}^{4 t}
\]
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| \[
{} -y+y^{\prime } = 2 \cos \left (5 t \right )
\]
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| \[
{} y^{\prime \prime }+5 y^{\prime }+4 y = 0
\]
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| \[
{} y^{\prime \prime }-4 y^{\prime } = 6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t}
\]
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| \[
{} y^{\prime \prime }+y = \sqrt {2}\, \sin \left (\sqrt {2}\, t \right )
\]
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| \[
{} y^{\prime \prime }+9 y = {\mathrm e}^{t}
\]
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| \[
{} 2 y^{\prime \prime \prime }+3 y^{\prime \prime }-3 y^{\prime }-2 y = {\mathrm e}^{-t}
\]
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| \[
{} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = \sin \left (3 t \right )
\]
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| \[
{} y+y^{\prime } = {\mathrm e}^{-3 t} \cos \left (2 t \right )
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+5 y = 0
\]
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| \[
{} y^{\prime }+4 y = {\mathrm e}^{-4 t}
\]
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| \[
{} -y+y^{\prime } = 1+t \,{\mathrm e}^{t}
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = 0
\]
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| \[
{} y^{\prime \prime }-4 y^{\prime }+4 y = t^{3} {\mathrm e}^{2 t}
\]
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| \[
{} y^{\prime \prime }-6 y^{\prime }+9 y = t
\]
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| \[
{} y^{\prime \prime }-4 y^{\prime }+4 y = t^{3}
\]
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| \[
{} y^{\prime \prime }-6 y^{\prime }+13 y = 0
\]
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| \[
{} 2 y^{\prime \prime }+20 y^{\prime }+51 y = 0
\]
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| \[
{} y^{\prime \prime }-y = {\mathrm e}^{t} \cos \left (t \right )
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+5 y = t +1
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = 0
\]
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| \[
{} y^{\prime \prime }+8 y^{\prime }+20 y = 0
\]
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| \[
{} y+y^{\prime } = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 5 & 1\le t \end {array}\right .
\]
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| \[
{} y+y^{\prime } = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .
\]
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| \[
{} y+y^{\prime } = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+4 y = \operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right )
\]
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| \[
{} y^{\prime \prime }-5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right )
\]
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| \[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+4 y^{\prime }+3 y = 1-\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -4\right )+\operatorname {Heaviside}\left (t -6\right )
\]
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| \[
{} y+y^{\prime } = t \sin \left (t \right )
\]
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| \[
{} -y+y^{\prime } = t \,{\mathrm e}^{t} \sin \left (t \right )
\]
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| \[
{} y^{\prime \prime }+9 y = \cos \left (3 t \right )
\]
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| \[
{} y^{\prime \prime }+y = \sin \left (t \right )
\]
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| \[
{} y^{\prime \prime }+16 y = \left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ \sin \left (t \right ) & \frac {\pi }{2}\le t \end {array}\right .
\]
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| \[
{} t y^{\prime \prime }-y^{\prime } = 2 t^{2}
\]
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| \[
{} 2 y^{\prime \prime }+t y^{\prime }-2 y = 10
\]
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| \[
{} y^{\prime \prime }+y = \sin \left (t \right )+t \sin \left (t \right )
\]
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| \[
{} y^{\prime }-3 y = \delta \left (t -2\right )
\]
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| \[
{} y+y^{\prime } = \delta \left (t -1\right )
\]
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| \[
{} y^{\prime \prime }+y = \delta \left (t -2 \pi \right )
\]
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| \[
{} y^{\prime \prime }+16 y = \delta \left (t -2 \pi \right )
\]
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| \[
{} y^{\prime \prime }+y = \delta \left (t -\frac {\pi }{2}\right )+\delta \left (t -\frac {3 \pi }{2}\right )
\]
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| \[
{} y^{\prime \prime }+y = \delta \left (t -2 \pi \right )+\delta \left (t -4 \pi \right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime } = \delta \left (t -1\right )
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime } = 1+\delta \left (t -2\right )
\]
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| \[
{} y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -2 \pi \right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = \delta \left (t -1\right )
\]
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| \[
{} y^{\prime \prime }+4 y^{\prime }+13 y = \delta \left (t -\pi \right )+\delta \left (t -3 \pi \right )
\]
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| \[
{} y^{\prime \prime }-7 y^{\prime }+6 y = {\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (t -4\right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+10 y = 0
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+10 y = \delta \left (t \right )
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+8 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-7 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right )-9 z \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )-y \left (t \right ), z^{\prime }\left (t \right ) = 10 x \left (t \right )+4 y \left (t \right )+3 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = -x \left (t \right )+z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+z \left (t \right )+t -1, y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )-z \left (t \right )-3 t^{2}, z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+z \left (t \right )+t^{2}-t +2]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right )+{\mathrm e}^{-t} \sin \left (2 t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+9 z \left (t \right )+4 \,{\mathrm e}^{-t} \cos \left (2 t \right ), z^{\prime }\left (t \right ) = y \left (t \right )+6 z \left (t \right )-{\mathrm e}^{-t}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )+2 y \left (t \right )+{\mathrm e}^{t}, y^{\prime }\left (t \right ) = -x \left (t \right )+3 y \left (t \right )-{\mathrm e}^{t}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 7 x \left (t \right )+5 y \left (t \right )-9 z \left (t \right )-8 \,{\mathrm e}^{-2 t}, y^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )+z \left (t \right )+2 \,{\mathrm e}^{5 t}, z^{\prime }\left (t \right ) = -2 y \left (t \right )+3 z \left (t \right )+{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-2 t}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+2 z \left (t \right )+{\mathrm e}^{-t}-3 t, y^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )+z \left (t \right )+2 \,{\mathrm e}^{-t}+t, z^{\prime }\left (t \right ) = -2 x \left (t \right )+5 y \left (t \right )+6 z \left (t \right )+2 \,{\mathrm e}^{-t}-t]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-7 y \left (t \right )+4 \sin \left (t \right )+\left (t -4\right ) {\mathrm e}^{4 t}, y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+8 \sin \left (t \right )+\left (2 t +1\right ) {\mathrm e}^{4 t}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-7 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+5 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+4 y \left (t \right )]
\]
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| \[
{} \left [x^{\prime }\left (t \right ) = -x \left (t \right )+\frac {y \left (t \right )}{4}, y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )\right ]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )-y \left (t \right ), z^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )-z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), z^{\prime }\left (t \right ) = -2 x \left (t \right )-z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+3 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )]
\]
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| \[
{} \left [x^{\prime }\left (t \right ) = -4 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -\frac {5 x \left (t \right )}{2}+2 y \left (t \right )\right ]
\]
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| \[
{} \left [x^{\prime }\left (t \right ) = -\frac {5 x \left (t \right )}{2}+2 y \left (t \right ), y^{\prime }\left (t \right ) = \frac {3 x \left (t \right )}{4}-2 y \left (t \right )\right ]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 10 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )-12 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -6 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right ), z^{\prime }\left (t \right ) = y \left (t \right )-z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-7 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+10 y \left (t \right )+4 z \left (t \right ), z^{\prime }\left (t \right ) = 5 y \left (t \right )+2 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = 3 y \left (t \right )-z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+z \left (t \right )]
\]
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| \[
{} \left [x^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = \frac {3 x \left (t \right )}{4}-\frac {3 y \left (t \right )}{2}+3 z \left (t \right ), z^{\prime }\left (t \right ) = \frac {x \left (t \right )}{8}+\frac {y \left (t \right )}{4}-\frac {z \left (t \right )}{2}\right ]
\]
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| \[
{} \left [x^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = \frac {3 x \left (t \right )}{4}-\frac {3 y \left (t \right )}{2}+3 z \left (t \right ), z^{\prime }\left (t \right ) = \frac {x \left (t \right )}{8}+\frac {y \left (t \right )}{4}-\frac {z \left (t \right )}{2}\right ]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+4 y \left (t \right )+2 z \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )-2 z \left (t \right ), z^{\prime }\left (t \right ) = 6 z \left (t \right )]
\]
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| \[
{} \left [x^{\prime }\left (t \right ) = \frac {x \left (t \right )}{2}, y^{\prime }\left (t \right ) = x \left (t \right )-\frac {y \left (t \right )}{2}\right ]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+4 z \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+z \left (t \right )]
\]
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| \[
{} \left [x^{\prime }\left (t \right ) = \frac {9 x \left (t \right )}{10}+\frac {21 y \left (t \right )}{10}+\frac {16 z \left (t \right )}{5}, y^{\prime }\left (t \right ) = \frac {7 x \left (t \right )}{10}+\frac {13 y \left (t \right )}{2}+\frac {21 z \left (t \right )}{5}, z^{\prime }\left (t \right ) = \frac {11 x \left (t \right )}{10}+\frac {17 y \left (t \right )}{10}+\frac {17 z \left (t \right )}{5}\right ]
\]
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| \[
{} \left [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{3} \left (t \right )-\frac {9 x_{4} \left (t \right )}{5}, x_{2}^{\prime }\left (t \right ) = \frac {51 x_{2} \left (t \right )}{10}-x_{4} \left (t \right )+3 x_{5} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = x_{2} \left (t \right )-\frac {31 x_{3} \left (t \right )}{10}+4 x_{4} \left (t \right ), x_{5}^{\prime }\left (t \right ) = -\frac {14 x_{1} \left (t \right )}{5}+\frac {3 x_{4} \left (t \right )}{2}-x_{5} \left (t \right )\right ]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 9 x \left (t \right )-3 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -6 x \left (t \right )+5 y \left (t \right ), y^{\prime }\left (t \right ) = -5 x \left (t \right )+4 y \left (t \right )]
\]
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|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+5 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|