| # | ODE | Mathematica | Maple | Sympy |
| \[
{} [x^{\prime }\left (t \right ) = 12 x \left (t \right )-9 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )+4 z \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = 4 x \left (t \right )+2 y \left (t \right )+3 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = 2 y \left (t \right )+5 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = 3 y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = -y \left (t \right )+z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+2 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 4 y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = 4 z \left (t \right )]
\]
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{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+6 y \left (t \right )]
\]
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{} [x^{\prime }\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 )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 6 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )+5 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+6 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )-4 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-8 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = z \left (t \right ), y^{\prime }\left (t \right ) = -z \left (t \right ), z^{\prime }\left (t \right ) = y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )+2 z \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+6 z \left (t \right ), z^{\prime }\left (t \right ) = -4 x \left (t \right )-3 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-12 y \left (t \right )-14 z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )-3 z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-2 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+3 y \left (t \right )-7, y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )+5]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )+9 y \left (t \right )+2, y^{\prime }\left (t \right ) = -x \left (t \right )+11 y \left (t \right )+6]
\]
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| \[
{} x^{2} {y^{\prime }}^{2}-y^{2} = 0
\]
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| \[
{} x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y = 0
\]
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| \[
{} x^{2} {y^{\prime }}^{2}-5 y y^{\prime } x +6 y^{2} = 0
\]
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| \[
{} x^{2} {y^{\prime }}^{2}+x y^{\prime }-y^{2}-y = 0
\]
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| \[
{} x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-x y = 0
\]
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| \[
{} {y^{\prime }}^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y = 0
\]
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| \[
{} x {y^{\prime }}^{2}-\left (x y+1\right ) y^{\prime }+y = 0
\]
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| \[
{} {y^{\prime }}^{2}-x^{2} y^{2} = 0
\]
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| \[
{} \left (x +y\right )^{2} {y^{\prime }}^{2} = y^{2}
\]
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| \[
{} y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-x y = 0
\]
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| \[
{} {y^{\prime }}^{2}-y^{\prime } x y \left (x +y\right )+x^{3} y^{3} = 0
\]
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| \[
{} \left (4 x -y\right ) {y^{\prime }}^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y = 0
\]
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| \[
{} \left (x -y\right )^{2} {y^{\prime }}^{2} = y^{2}
\]
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| \[
{} x y {y^{\prime }}^{2}+\left (x y^{2}-1\right ) y^{\prime }-y = 0
\]
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| \[
{} \left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2} = 4 x^{2} y^{2}
\]
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| \[
{} \left (x +y\right )^{2} {y^{\prime }}^{2}+\left (2 y^{2}+x y-x^{2}\right ) y^{\prime }+y \left (y-x \right ) = 0
\]
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| \[
{} x y \left (x^{2}+y^{2}\right ) \left ({y^{\prime }}^{2}-1\right ) = y^{\prime } \left (x^{4}+x^{2} y^{2}+y^{4}\right )
\]
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| \[
{} x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+x y\right ) y^{\prime }-x y = 0
\]
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| \[
{} x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1 = 0
\]
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| \[
{} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2} = 0
\]
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| \[
{} 3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0
\]
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| \[
{} {y^{\prime }}^{2}-x y^{\prime }-y = 0
\]
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| \[
{} {y^{\prime }}^{2}-x y^{\prime }+y = 0
\]
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| \[
{} {y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0
\]
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| \[
{} 4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0
\]
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| \[
{} 4 y^{3} {y^{\prime }}^{2}+4 x y^{\prime }+y = 0
\]
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| \[
{} {y^{\prime }}^{3}+x {y^{\prime }}^{2}-y = 0
\]
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| \[
{} y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y = 0
\]
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| \[
{} {y^{\prime }}^{2}+x^{3} y^{\prime }-2 x^{2} y = 0
\]
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| \[
{} {y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0
\]
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| \[
{} 2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4} = 0
\]
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| \[
{} {y^{\prime }}^{2}-x y^{\prime }+y = 0
\]
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| \[
{} y = x y^{\prime }+k {y^{\prime }}^{2}
\]
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| \[
{} x^{8} {y^{\prime }}^{2}+3 x y^{\prime }+9 y = 0
\]
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| \[
{} x^{4} {y^{\prime }}^{2}+2 x^{3} y y^{\prime }-4 = 0
\]
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| \[
{} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2} = 0
\]
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{} 3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0
\]
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{} x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }+1-y = 0
\]
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| \[
{} y^{\prime } \left (x y^{\prime }-y+k \right )+a = 0
\]
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| \[
{} x^{6} {y^{\prime }}^{3}-3 x y^{\prime }-3 y = 0
\]
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| \[
{} y = x^{6} {y^{\prime }}^{3}-x y^{\prime }
\]
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{} {y^{\prime }}^{4} x -2 {y^{\prime }}^{3} y+12 x^{3} = 0
\]
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{} x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1 = 0
\]
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| \[
{} {y^{\prime }}^{2}-x y^{\prime }-y = 0
\]
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{} 2 {y^{\prime }}^{3}+x y^{\prime }-2 y = 0
\]
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{} 2 {y^{\prime }}^{2}+x y^{\prime }-2 y = 0
\]
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{} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\]
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{} 4 x {y^{\prime }}^{2}-3 y y^{\prime }+3 = 0
\]
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| \[
{} {y^{\prime }}^{3}-x y^{\prime }+2 y = 0
\]
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| \[
{} 5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y = 0
\]
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| \[
{} 2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y = 0
\]
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{} 5 {y^{\prime }}^{2}+3 x y^{\prime }-y = 0
\]
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{} {y^{\prime }}^{2}+3 x y^{\prime }-y = 0
\]
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| \[
{} y = x y^{\prime }+x^{3} {y^{\prime }}^{2}
\]
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| \[
{} y^{\prime \prime } = x {y^{\prime }}^{3}
\]
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{} x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime } = 0
\]
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{} x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime } = 0
\]
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| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\]
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| \[
{} y^{2} y^{\prime \prime }+{y^{\prime }}^{3} = 0
\]
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| \[
{} \left (1+y\right ) y^{\prime \prime } = {y^{\prime }}^{2}
\]
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| \[
{} 2 a y^{\prime \prime }+{y^{\prime }}^{3} = 0
\]
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{} x y^{\prime \prime } = y^{\prime }+x^{5}
\]
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{} x y^{\prime \prime }+y^{\prime }+x = 0
\]
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| \[
{} y^{\prime \prime } = 2 {y^{\prime }}^{3} y
\]
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| \[
{} -{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime }+\beta ^{2} y = 0
\]
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| \[
{} {y^{\prime }}^{3}+y y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime } \cos \left (x \right ) = y^{\prime }
\]
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{} y^{\prime \prime } = x {y^{\prime }}^{2}
\]
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{} y^{\prime \prime } = x {y^{\prime }}^{2}
\]
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{} y^{\prime \prime } = -{\mathrm e}^{-2 y}
\]
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{} y^{\prime \prime } = -{\mathrm e}^{-2 y}
\]
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{} 2 y^{\prime \prime } = \sin \left (2 y\right )
\]
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| \[
{} 2 y^{\prime \prime } = \sin \left (2 y\right )
\]
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| \[
{} -x^{2} y^{\prime }+x^{3} y^{\prime \prime } = -x^{2}+3
\]
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{} y^{\prime \prime } = {y^{\prime }}^{2}
\]
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{} y^{\prime \prime } = {\mathrm e}^{x} {y^{\prime }}^{2}
\]
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| \[
{} 2 y^{\prime \prime } = {y^{\prime }}^{3} \sin \left (2 x \right )
\]
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| \[
{} {y^{\prime }}^{2}+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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