| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }-\left (x -2\right ) y^{\prime }+2 y = 0
\]
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| \[
{} y^{\prime \prime }+x y^{\prime }+\left (2 x -1\right ) y = 0
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| \[
{} y^{\prime \prime }+x y^{\prime }+\left (2 x -1\right ) y = 0
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| \[
{} y^{\prime \prime }-2 x y = 0
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| \[
{} y^{\prime \prime }+x y = 2
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| \[
{} \left (x^{2}+4\right ) y^{\prime \prime }+x y = x +2
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| \[
{} y^{\prime \prime }+\left (x -1\right ) y = {\mathrm e}^{x}
\]
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| \[
{} n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
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| \[
{} \left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }-y = 0
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| \[
{} y^{\prime \prime }-x y = 0
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| \[
{} y^{\prime \prime }-x y = 0
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| \[
{} y^{\prime \prime }-x^{2} y^{\prime }+\left (x +2\right ) y = 0
\]
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| \[
{} \left (x^{2}+4\right ) y^{\prime \prime }+y = x
\]
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| \[
{} y^{\prime \prime }-\left (x -1\right ) y^{\prime } = x^{2}-2 x
\]
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| \[
{} y^{\prime \prime }-x y^{\prime } = {\mathrm e}^{-x}
\]
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| \[
{} y^{\prime \prime }-2 x y^{\prime }+x^{2} y = 0
\]
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| \[
{} y^{\prime \prime }-2 x y = x^{2}
\]
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| \[
{} 8 x^{2} y^{\prime \prime }+10 x y^{\prime }+\left (x -1\right ) y = 0
\]
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| \[
{} 2 x^{2} y^{\prime \prime }+7 x \left (1+x \right ) y^{\prime }-3 y = 0
\]
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| \[
{} 3 x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+2 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+y \left (x^{2}-1\right ) = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-2 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+x \,{\mathrm e}^{x} y^{\prime }+\left (x^{3}-1\right ) y = 0
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| \[
{} -b y a +\left (c -\left (1+a +b \right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime } = 0
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| \[
{} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (1-x \right ) y = 0
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| \[
{} 2 x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+y = 0
\]
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| \[
{} 3 x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}+2\right ) y = 0
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| \[
{} -y+y^{\prime }+x y^{\prime \prime } = 0
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+x^{3} y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y = 0
\]
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| \[
{} x y^{\prime \prime }-y^{\prime } \left (1+x \right )-y = 0
\]
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| \[
{} 4 x^{2} y^{\prime \prime }+\left (2 x^{2}+4 x \right ) y^{\prime }+\left (3 x -1\right ) y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+\left (3 x -1\right ) y = 0
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| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y = 0
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+y \left (x^{2}-1\right ) = 0
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| \[
{} x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+\left (-n^{2}+x^{2}+1\right ) y = 0
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| \[
{} x y^{\prime \prime }-3 y^{\prime }+x y = 0
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| \[
{} y^{\prime }-5 y = 0
\]
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| \[
{} y^{\prime }-5 y = {\mathrm e}^{5 x}
\]
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| \[
{} y^{\prime }-5 y = 0
\]
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| \[
{} y^{\prime }+y = \sin \left (x \right )
\]
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| \[
{} 4 y+y^{\prime \prime } = 0
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| \[
{} y^{\prime \prime }-3 y^{\prime }+4 y = 0
\]
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| \[
{} y^{\prime \prime }-y^{\prime }-2 y = 4 t^{2}
\]
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| \[
{} y^{\prime \prime }+4 y^{\prime }+8 y = \sin \left (t \right )
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-t}
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = f \left (t \right )
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| \[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & t <1 \\ 2 & 1\le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime \prime }+y^{\prime } = {\mathrm e}^{t}
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| \[
{} y^{\prime }+2 y = 0
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| \[
{} y^{\prime }+2 y = 2
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| \[
{} y^{\prime }+2 y = {\mathrm e}^{t}
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| \[
{} y^{\prime }+2 y = 0
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| \[
{} y^{\prime }+5 y = 0
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| \[
{} y^{\prime \prime }-y = 0
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| \[
{} y^{\prime \prime }-y = \sin \left (t \right )
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| \[
{} y^{\prime \prime }-y = {\mathrm e}^{t}
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| \[
{} y^{\prime \prime }+2 y^{\prime }-3 y = \sin \left (2 t \right )
\]
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| \[
{} y^{\prime \prime }+y = \sin \left (t \right )
\]
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| \[
{} y^{\prime \prime }+y^{\prime }+y = \sin \left (t \right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-2 t}
\]
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| \[
{} y^{\prime \prime }+5 y^{\prime }-3 y = \operatorname {Heaviside}\left (t -4\right )
\]
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| \[
{} y^{\prime \prime }+y = 0
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| \[
{} y^{\prime \prime \prime }-y = 5
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| \[
{} y^{\prime \prime \prime \prime }-y = 0
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| \[
{} [y^{\prime }\left (t \right )+z \left (t \right ) = t, z^{\prime }\left (t \right )+4 y \left (t \right ) = 0]
\]
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| \[
{} [w^{\prime }\left (t \right )+y \left (t \right ) = \sin \left (t \right ), y^{\prime }\left (t \right )-z \left (t \right ) = {\mathrm e}^{t}, w \left (t \right )+y \left (t \right )+z^{\prime }\left (t \right ) = 1]
\]
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| \[
{} [y^{\prime \prime }\left (t \right )+z \left (t \right )+y \left (t \right ) = 0, y^{\prime }\left (t \right )+z^{\prime }\left (t \right ) = 0]
\]
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| \[
{} [z^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right ) = \cos \left (t \right ), y^{\prime \prime }\left (t \right )-z \left (t \right ) = \sin \left (t \right )]
\]
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| \[
{} [w^{\prime \prime }\left (t \right )-y \left (t \right )+2 z \left (t \right ) = 3 \,{\mathrm e}^{-t}, -2 w^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )+z \left (t \right ) = 0, 2 w^{\prime }\left (t \right )-2 y \left (t \right )+z^{\prime }\left (t \right )+2 z^{\prime \prime }\left (t \right ) = 0]
\]
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| \[
{} [y^{\prime }\left (t \right )+z \left (t \right ) = t, z^{\prime }\left (t \right )-y \left (t \right ) = 0]
\]
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| \[
{} [y^{\prime }\left (t \right )-z \left (t \right ) = 0, y \left (t \right )-z^{\prime }\left (t \right ) = 0]
\]
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| \[
{} [w^{\prime }\left (t \right )-w \left (t \right )-2 y \left (t \right ) = 1, y^{\prime }\left (t \right )-4 w \left (t \right )-3 y \left (t \right ) = -1]
\]
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| \[
{} [w^{\prime }\left (t \right )-y \left (t \right ) = 0, w \left (t \right )+y^{\prime }\left (t \right )+z \left (t \right ) = 1, w \left (t \right )-y \left (t \right )+z^{\prime }\left (t \right ) = 2 \sin \left (t \right )]
\]
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| \[
{} [u^{\prime \prime }\left (t \right )-2 v \left (t \right ) = 2, u \left (t \right )+v^{\prime }\left (t \right ) = 5 \,{\mathrm e}^{2 t}+1]
\]
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| \[
{} [w^{\prime \prime }\left (t \right )-2 z \left (t \right ) = 0, w^{\prime }\left (t \right )+y^{\prime }\left (t \right )-z \left (t \right ) = 2 t, w^{\prime }\left (t \right )-2 y \left (t \right )+z^{\prime \prime }\left (t \right ) = 0]
\]
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| \[
{} [w^{\prime \prime }\left (t \right )+y \left (t \right )+z \left (t \right ) = -1, w \left (t \right )+y^{\prime \prime }\left (t \right )-z \left (t \right ) = 0, -w \left (t \right )-y^{\prime }\left (t \right )+z^{\prime \prime }\left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )-2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )-2 y \left (t \right )+{\mathrm e}^{t}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+3]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -9 x \left (t \right )+6 y \left (t \right )+t]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )-5 z \left (t \right )+3, z^{\prime }\left (t \right ) = y \left (t \right )+2 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 9 x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+4]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+4]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+4]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+9 \,{\mathrm e}^{-t}]
\]
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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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| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 6 t]
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }-3 y = 0
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }-3 y = 9 x
\]
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| \[
{} y^{\prime \prime }+y = 0
\]
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| \[
{} y^{\prime \prime }+y = x
\]
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| \[
{} y^{\prime \prime }+y = 0
\]
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