| # | ODE | Mathematica | Maple | Sympy |
| \[
{} [2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right ) = 1, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )-y \left (t \right ) = t]
\]
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{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\]
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{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )+3 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 ) = 5 x \left (t \right )+2 y \left (t \right )+5 t, y^{\prime }\left (t \right ) = 3 x \left (t \right )+4 y \left (t \right )+17 t]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )]
\]
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{} [x^{\prime }\left (t \right ) = 5 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 ) = -2 x \left (t \right )+7 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 ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 7 x \left (t \right )+4 y \left (t \right )]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+3 y \left (t \right )-4 z \left (t \right ), z^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )-4 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = -3 x \left (t \right )-6 y \left (t \right )+6 z \left (t \right )]
\]
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| \[
{} -y+y^{\prime } = {\mathrm e}^{3 t}
\]
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| \[
{} y+y^{\prime } = 2 \sin \left (t \right )
\]
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| \[
{} y^{\prime \prime }-5 y^{\prime }+6 y = 0
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| \[
{} y^{\prime \prime }+y^{\prime }-12 y = 0
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| \[
{} y^{\prime \prime }+4 y = 8
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| \[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 0
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| \[
{} y^{\prime \prime }-y^{\prime }-2 y = 18 \,{\mathrm e}^{-t} \sin \left (3 t \right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = t \,{\mathrm e}^{-2 t}
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| \[
{} y^{\prime \prime }+7 y^{\prime }+10 y = 4 t \,{\mathrm e}^{-3 t}
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| \[
{} y^{\prime \prime }-8 y^{\prime }+15 y = 9 t \,{\mathrm e}^{2 t}
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| \[
{} y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y = 20 \sin \left (t \right )
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| \[
{} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 36 t \,{\mathrm e}^{4 t}
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 2 & 0<t <4 \\ 0 & 4<t \end {array}\right .
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| \[
{} y^{\prime \prime }+5 y^{\prime }+6 y = \left \{\begin {array}{cc} 6 & 0<t <2 \\ 0 & 2<t \end {array}\right .
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| \[
{} y^{\prime \prime }+4 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0<t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right .
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{} y^{\prime \prime }+6 y^{\prime }+8 y = \left \{\begin {array}{cc} 3 & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right .
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| \[
{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} -4 t +8 \pi & 0<t <2 \pi \\ 0 & 2<t \end {array}\right .
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{} y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0<t <\pi \\ \pi & \pi <t \end {array}\right .
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| \[
{} t x^{\prime \prime }-2 x^{\prime }+9 t^{5} x = 0
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| \[
{} t^{3} x^{\prime \prime \prime }-3 t^{2} x^{\prime \prime }+6 t x^{\prime }-6 x = 0
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| \[
{} \left (t^{3}-2 t^{2}\right ) x^{\prime \prime }-\left (t^{3}+2 t^{2}-6 t \right ) x^{\prime }+\left (3 t^{2}-6\right ) x = 0
\]
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| \[
{} t^{3} x^{\prime \prime \prime }-\left (3+t \right ) t^{2} x^{\prime \prime }+2 t \left (3+t \right ) x^{\prime }-2 \left (3+t \right ) x = 0
\]
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| \[
{} t^{2} x^{\prime \prime }+3 t x^{\prime }+3 x = 0
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| \[
{} \left (2 t +1\right ) x^{\prime \prime }+t^{3} x^{\prime }+x = 0
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| \[
{} t^{2} x^{\prime \prime }+\left (2 t^{3}+7 t \right ) x^{\prime }+\left (8 t^{2}+8\right ) x = 0
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| \[
{} t^{3} x^{\prime \prime }-\left (t^{3}+2 t^{2}-t \right ) x^{\prime }+\left (t^{2}+t -1\right ) x = 0
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| \[
{} t^{3} x^{\prime \prime }+3 t^{2} x^{\prime }+x = 0
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| \[
{} \sin \left (t \right ) x^{\prime \prime }+\cos \left (t \right ) x^{\prime }+2 x = 0
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| \[
{} \frac {\left (t +1\right ) x^{\prime \prime }}{t}-\frac {x^{\prime }}{t^{2}}+\frac {x}{t^{3}} = 0
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| \[
{} t^{2} x^{\prime \prime }+t x^{\prime }+x = 0
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| \[
{} \left (t^{4}+t^{2}\right ) x^{\prime \prime }+2 t^{3} x^{\prime }+3 x = 0
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| \[
{} x^{\prime \prime }-\tan \left (t \right ) x^{\prime }+x = 0
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| \[
{} f \left (t \right ) x^{\prime \prime }+x g \left (t \right ) = 0
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| \[
{} x^{\prime \prime }+\left (t +1\right ) x = 0
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| \[
{} y^{\prime \prime }+\lambda y = 0
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| \[
{} y^{\prime \prime }+\lambda y = 0
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| \[
{} y^{\prime \prime }+\lambda y = 0
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| \[
{} y^{\prime \prime }+\lambda y = 0
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| \[
{} y^{\prime }+x y^{\prime \prime }+\frac {\lambda y}{x} = 0
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| \[
{} y^{\prime }+x y^{\prime \prime }+\frac {\lambda y}{x} = 0
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| \[
{} 2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }+\frac {\lambda y}{x^{2}+1} = 0
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| \[
{} -\frac {6 y^{\prime } x}{\left (3 x^{2}+1\right )^{2}}+\frac {y^{\prime \prime }}{3 x^{2}+1}+\lambda \left (3 x^{2}+1\right ) y = 0
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
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{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )]
\]
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{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+2 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 ) = x \left (t \right )-2 y \left (t \right )]
\]
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{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-4 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 )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+5 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 )+5 y \left (t \right )]
\]
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{} [x^{\prime }\left (t \right ) = x \left (t \right )+7 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+5 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 ) = 3 x \left (t \right )-y \left (t \right )]
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{} [x^{\prime }\left (t \right ) = a x \left (t \right )+b y \left (t \right ), y^{\prime }\left (t \right ) = c x \left (t \right )+d y \left (t \right )]
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| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-4 y \left (t \right )-x \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+4 y \left (t \right )-y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )]
\]
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| \[
{} \left [x^{\prime }\left (t \right ) = y \left (t \right )+\frac {x \left (t \right ) \left (1-x \left (t \right )^{2}-y \left (t \right )^{2}\right )}{\sqrt {x \left (t \right )^{2}+y \left (t \right )^{2}}}, y^{\prime }\left (t \right ) = -x \left (t \right )+\frac {y \left (t \right ) \left (1-x \left (t \right )^{2}-y \left (t \right )^{2}\right )}{\sqrt {x \left (t \right )^{2}+y \left (t \right )^{2}}}\right ]
\]
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| \[
{} x^{\prime \prime }+x^{4} x^{\prime }-x^{\prime }+x = 0
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{} x^{\prime \prime }+x^{\prime }+{x^{\prime }}^{3}+x = 0
\]
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{} x^{\prime \prime }+\left (x^{4}+x^{2}\right ) x^{\prime }+x^{3}+x = 0
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{} x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3} = 0
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{} x^{\prime \prime }+\left (1+x^{2}\right ) x^{\prime }+x^{3} = 0
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right )^{2}, y^{\prime }\left (t \right ) = 2 y \left (t \right )-y \left (t \right )^{2}]
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| \[
{} x^{\prime } = \sin \left (t \right )+\cos \left (t \right )
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{} y^{\prime } = \frac {1}{x^{2}-1}
\]
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{} u^{\prime } = 4 t \ln \left (t \right )
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{} z^{\prime } = x \,{\mathrm e}^{-2 x}
\]
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{} T^{\prime } = {\mathrm e}^{-t} \sin \left (2 t \right )
\]
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{} x^{\prime } = \sec \left (t \right )^{2}
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{} y^{\prime } = x -\frac {1}{3} x^{3}
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{} x^{\prime } = 2 \sin \left (t \right )^{2}
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| \[
{} x V^{\prime } = x^{2}+1
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| \[
{} x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t} = {\mathrm e}^{-t}
\]
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{} x^{\prime } = 1-x
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{} x^{\prime } = x \left (2-x\right )
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{} x^{\prime } = \left (1+x\right ) \left (2-x\right ) \sin \left (x\right )
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{} x^{\prime } = -x \left (1-x\right ) \left (2-x\right )
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{} x^{\prime } = x^{2}-x^{4}
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| \[
{} x^{\prime } = t^{3} \left (1-x\right )
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