| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }+2 y^{\prime }+\sin \left (t \right ) y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y = t^{2} {\mathrm e}^{-t}
\]
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| \[
{} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y = 2 t
\]
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| \[
{} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y = 0
\]
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| \[
{} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y = 2 t
\]
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| \[
{} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y = 2 t
\]
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| \[
{} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y = 2 t
\]
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| \[
{} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y = 2 t
\]
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| \[
{} \left (t -1\right ) y^{\prime \prime }-t y^{\prime }+y = 2 t \,{\mathrm e}^{-t}
\]
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| \[
{} \left (t -1\right ) y^{\prime \prime }-t y^{\prime }+y = 0
\]
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| \[
{} \left (t -1\right ) y^{\prime \prime }-t y^{\prime }+y = 2 t \,{\mathrm e}^{-t}
\]
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| \[
{} \left (t -1\right ) y^{\prime \prime }-t y^{\prime }+y = 2 t \,{\mathrm e}^{-t}
\]
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| \[
{} \left (t -1\right ) y^{\prime \prime }-t y^{\prime }+y = 2 t \,{\mathrm e}^{-t}
\]
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| \[
{} \left (t -1\right ) y^{\prime \prime }-t y^{\prime }+y = 2 t \,{\mathrm e}^{-t}
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }-2 y = \frac {t^{2}+1}{-t^{2}+1}
\]
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| \[
{} \sin \left (t \right ) y^{\prime \prime }+y = \cos \left (t \right )
\]
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| \[
{} \left (t^{2}+1\right ) y^{\prime \prime }-t y^{\prime }+t^{2} y = \cos \left (t \right )
\]
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| \[
{} y^{\prime \prime }+\sqrt {t}\, y^{\prime }-\sqrt {t -3}\, y = 0
\]
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| \[
{} t \left (t^{2}-4\right ) y^{\prime \prime }+y = {\mathrm e}^{t}
\]
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| \[
{} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = 0
\]
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| \[
{} y^{\prime \prime }+a_{1} \left (t \right ) y^{\prime }+a_{0} \left (t \right ) y = f \left (t \right )
\]
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| \[
{} \left (t -1\right ) y^{\prime \prime }-t y^{\prime }+y = 0
\]
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| \[
{} \left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = 0
\]
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| \[
{} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y = 0
\]
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| \[
{} t y^{\prime \prime }+\left (t +1\right ) y^{\prime }+y = 0
\]
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| \[
{} t y^{\prime \prime }+\left (2+4 t \right ) y^{\prime }+\left (4+4 t \right ) y = 0
\]
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| \[
{} t y^{\prime \prime }-4 y^{\prime }+t y = 0
\]
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| \[
{} t y^{\prime \prime }+\left (2+2 t \right ) y^{\prime }+\left (t +2\right ) y = 0
\]
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| \[
{} -t y^{\prime \prime }+\left (t -2\right ) y^{\prime }+y = 0
\]
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| \[
{} t y^{\prime \prime }+\left (2-5 t \right ) y^{\prime }+\left (6 t -5\right ) y = 0
\]
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| \[
{} t y^{\prime \prime \prime }+3 y^{\prime \prime }+t y^{\prime }+y = 0
\]
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| \[
{} t y^{\prime \prime }+\left (t +2\right ) y^{\prime }+y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 0
\]
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| \[
{} t y^{\prime \prime }-2 \left (t +1\right ) y^{\prime }+4 y = 0
\]
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| \[
{} y^{\prime \prime }-2 \sec \left (t \right )^{2} y = 0
\]
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| \[
{} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y = 0
\]
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| \[
{} y^{\prime \prime }-\tan \left (t \right ) y^{\prime }-\sec \left (t \right )^{2} y = 0
\]
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| \[
{} \left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\]
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| \[
{} \left (1+\cos \left (2 t \right )\right ) y^{\prime \prime }-4 y = 0
\]
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| \[
{} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\]
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| \[
{} y^{\prime \prime }-4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 t}}{t^{2}+1}
\]
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| \[
{} y^{\prime \prime }-\tan \left (t \right ) y^{\prime }-\sec \left (t \right )^{2} y = t
\]
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| \[
{} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y = t^{2} {\mathrm e}^{-t}
\]
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| \[
{} t y^{\prime \prime }-y^{\prime }+4 t^{3} y = 4 t^{5}
\]
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| \[
{} -y+y^{\prime } = \left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t <4 \\ 0 & 4\le t <\infty \end {array}\right .
\]
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| \[
{} 3 y+y^{\prime } = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t <\infty \end {array}\right .
\]
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| \[
{} -y+y^{\prime } = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ t -1 & 1\le t <2 \\ -t +3 & 2\le t <3 \\ 0 & 3\le t <\infty \end {array}\right .
\]
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| \[
{} y^{\prime \prime }-4 y^{\prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le t <2 \\ 4 & 2\le t <\infty \end {array}\right .
\]
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| \[
{} y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ -3 & 1\le t \end {array}\right .
\]
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| \[
{} y^{\prime }+5 y = \left \{\begin {array}{cc} -5 & 0\le t <1 \\ 5 & 1\le t \end {array}\right .
\]
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| \[
{} y^{\prime }-3 y = \left \{\begin {array}{cc} 0 & 0\le t <2 \\ 2 & 2\le t <3 \\ 0 & 3\le t \end {array}\right .
\]
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| \[
{} y^{\prime }+2 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\]
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| \[
{} y^{\prime }-4 y = \left \{\begin {array}{cc} 12 \,{\mathrm e}^{t} & 0\le t <1 \\ 12 \,{\mathrm e} & 1\le t \end {array}\right .
\]
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| \[
{} 3 y+y^{\prime } = \left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }-5 y^{\prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <5 \\ 0 & 5\le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+5 y^{\prime }+6 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 6 & 1\le t <3 \\ 0 & 3\le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = \left \{\begin {array}{cc} {\mathrm e}^{-t} & 0\le t <4 \\ 0 & 4\le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+\frac {\left (1-t \right ) y^{\prime }}{t}+\frac {\left (1-\cos \left (t \right )\right ) y}{t^{3}} = 0
\]
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| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{t}+\frac {\left (1-t \right ) y}{t^{3}} = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+t \,{\mathrm e}^{t} y^{\prime }+4 \left (1-4 t \right ) y = 0
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right ) y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = t \sin \left (y_{1} \left (t \right )\right )-y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )+t \cos \left (y_{2} \left (t \right )\right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-y_{2} \left (t \right )+{\mathrm e}^{t}, y_{2}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )-2 y_{2} \left (t \right )+{\mathrm e}^{t}]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )+y_{2} \left (t \right )+{\mathrm e}^{t}, y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )+2 y_{2} \left (t \right )-{\mathrm e}^{t}]
\]
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| \[
{} \left [y_{1}^{\prime }\left (t \right ) = \frac {y_{1} \left (t \right )}{t}+1, y_{2}^{\prime }\left (t \right ) = \frac {y_{2} \left (t \right )}{t}+t\right ]
\]
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| \[
{} \left [y_{1}^{\prime }\left (t \right ) = -\frac {y_{2} \left (t \right )}{t}+1, y_{2}^{\prime }\left (t \right ) = \frac {y_{1} \left (t \right )}{t}+\frac {2 y_{2} \left (t \right )}{t}-1\right ]
\]
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