| # | ODE | Mathematica | Maple | Sympy |
| \[
{} 2 \left (x -y^{\prime }\right ) y^{\prime }-x \left (x +4 y^{\prime }\right ) y^{\prime \prime }+2 \left (x^{2}+1\right ) {y^{\prime \prime }}^{2} = 2 y
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{} 4 {y^{\prime }}^{2}-2 \left (3 x y^{\prime }+y\right ) y^{\prime \prime }+3 x^{2} {y^{\prime \prime }}^{2} = 0
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| \[
{} 6 y y^{\prime \prime }-6 \left (1-6 x \right ) x y^{\prime } y^{\prime \prime }+\left (2-9 x \right ) x^{2} {y^{\prime \prime }}^{2} = 36 x {y^{\prime }}^{2}
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| \[
{} h y^{2}+\operatorname {g1} y y^{\prime }+\operatorname {g0} {y^{\prime }}^{2}+\operatorname {f2} y y^{\prime \prime }+\operatorname {f1} y^{\prime } y^{\prime \prime }+\operatorname {f0} {y^{\prime \prime }}^{2} = 0
\]
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| \[
{} -{y^{\prime }}^{2}+4 {y^{\prime }}^{3} y+y y^{\prime \prime } = 0
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| \[
{} \left (1+{y^{\prime }}^{2}+y y^{\prime \prime }\right )^{2} = \left (1+{y^{\prime }}^{2}\right )^{3}
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| \[
{} {y^{\prime }}^{2} \left (1-b^{2} {y^{\prime }}^{2}\right )+2 b^{2} y {y^{\prime }}^{2} y^{\prime \prime }+\left (a^{2}-b^{2} y^{2}\right ) {y^{\prime \prime }}^{2} = 0
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{} \left (y^{2}-x^{2} {y^{\prime }}^{2}+x^{2} y y^{\prime \prime }\right )^{2} = 4 x y \left (x y^{\prime }-y\right )^{3}
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| \[
{} {y^{\prime \prime }}^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right )
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| \[
{} 32 y^{\prime \prime } \left (x y^{\prime \prime }-y^{\prime }\right )^{3}+\left (2 y y^{\prime \prime }-{y^{\prime }}^{2}\right )^{3} = 0
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| \[
{} f \left (y^{\prime \prime }\right )+x y^{\prime \prime } = y^{\prime }
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{} f \left (\frac {y^{\prime \prime }}{y^{\prime }}\right ) y^{\prime } = {y^{\prime }}^{2}-y y^{\prime \prime }
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{} f \left (y^{\prime \prime }, y^{\prime }-x y^{\prime \prime }, y-x y^{\prime }+\frac {x^{2} y^{\prime \prime }}{2}\right ) = 0
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{} y^{\prime } y^{\prime \prime } = a x {y^{\prime }}^{5}+3 {y^{\prime \prime }}^{2}
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{} y^{\prime \prime }+2 y^{\prime } = 0
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{} y^{\prime \prime }-3 y^{\prime }+2 y = 0
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{} y^{\prime \prime }-y = 0
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| \[
{} 6 y^{\prime \prime }-11 y^{\prime }+4 y = 0
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{} y^{\prime \prime }+2 y^{\prime }-y = 0
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{} y^{\prime \prime }-2 k y^{\prime }-2 y = 0
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| \[
{} y^{\prime \prime }+4 k y^{\prime }-12 k^{2} y = 0
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{} y^{\prime \prime }+4 y^{\prime }+4 y = 0
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{} y^{\prime \prime }-2 a y^{\prime }+a^{2} y = 0
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{} y^{\prime \prime }-2 y^{\prime }+5 y = 0
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{} y^{\prime \prime }-y^{\prime }+y = 0
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| \[
{} y^{\prime \prime }-4 y^{\prime }+20 y = 0
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| \[
{} y^{\prime \prime } = 0
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| \[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 0
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| \[
{} y^{\prime \prime }-2 y^{\prime }+5 y = 0
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| \[
{} y^{\prime \prime }-4 y^{\prime }+20 y = 0
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{} y^{\prime \prime }+3 y^{\prime }+2 y = 4
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{} y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x}
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{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{i x}
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{} y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (x \right )
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{} y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (x \right )
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{} y^{\prime \prime }+3 y^{\prime }+2 y = 8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right )
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| \[
{} y^{\prime \prime }+y^{\prime }+y = x^{2}
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{} y^{\prime \prime }-2 y^{\prime }-8 y = 9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x}
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{} y^{\prime \prime }-3 y^{\prime } = 2 \,{\mathrm e}^{2 x} \sin \left (x \right )
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{} y^{\prime \prime }+y^{\prime } = x^{2}+2 x
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{} y^{\prime \prime }+y^{\prime } = x +\sin \left (2 x \right )
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{} y^{\prime \prime }+y = 4 x \sin \left (x \right )
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{} y^{\prime \prime }+4 y = \sin \left (2 x \right ) x
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{} y^{\prime \prime }+2 y^{\prime }+y = x^{2} {\mathrm e}^{-x}
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{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-2 x}+x^{2}
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{} y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{-x}
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{} y^{\prime \prime }+y^{\prime }-6 y = x +{\mathrm e}^{2 x}
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{} y^{\prime \prime }+y = \sin \left (x \right )+{\mathrm e}^{-x}
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{} y^{\prime \prime }+y = \sin \left (x \right )^{2}
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{} y^{\prime \prime }+y = \sin \left (2 x \right ) \sin \left (x \right )
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{} y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 x}
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{} y^{\prime \prime }-y^{\prime }-2 y = 5 \sin \left (x \right )
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{} y^{\prime \prime }+9 y = 8 \cos \left (x \right )
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{} y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{x} \left (2 x -3\right )
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{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-x}
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{} y^{\prime \prime }+y = \sec \left (x \right )
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{} y^{\prime \prime }+y = \cot \left (x \right )
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{} y^{\prime \prime }+y = \sec \left (x \right )^{2}
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{} y^{\prime \prime }-y = \sin \left (x \right )^{2}
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{} y^{\prime \prime }+y = \sin \left (x \right )^{2}
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{} y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x}
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{} y^{\prime \prime }+2 y^{\prime }+y = x^{2} {\mathrm e}^{-x}
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{} y^{\prime \prime }+y = 4 x \sin \left (x \right )
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{} y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \ln \left (x \right )
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{} y^{\prime \prime }+y = \csc \left (x \right )
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{} y^{\prime \prime }+y = \tan \left (x \right )^{2}
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{} y^{\prime \prime }+2 y^{\prime }+y = \frac {{\mathrm e}^{-x}}{x}
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{} y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right )
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{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \ln \left (x \right )
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{} y^{\prime \prime }-3 y^{\prime }+2 y = \cos \left ({\mathrm e}^{-x}\right )
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{} x^{2} y^{\prime \prime }-x y^{\prime }+y = x
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{} y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = x \ln \left (x \right )
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{} x^{2} y^{\prime \prime }+x y^{\prime }-4 y = x^{3}
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{} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2} {\mathrm e}^{-x}
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{} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = \frac {1}{x}
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{} y^{\prime \prime } = 2 y y^{\prime }
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{} y^{3} y^{\prime \prime } = k
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{} y y^{\prime \prime } = {y^{\prime }}^{2}-1
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{} x^{2} y^{\prime \prime }+x y^{\prime } = 1
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{} x y^{\prime \prime }-y^{\prime } = x^{2}
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{} \left (1+y\right ) y^{\prime \prime } = 3 {y^{\prime }}^{2}
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{} r^{\prime \prime } = -\frac {k}{r^{2}}
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{} y^{\prime \prime } = \frac {3 k y^{2}}{2}
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{} y^{\prime \prime } = 2 k y^{3}
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{} y y^{\prime \prime }+{y^{\prime }}^{2}-y^{\prime } = 0
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{} r^{\prime \prime } = \frac {h^{2}}{r^{3}}-\frac {k}{r^{2}}
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{} -{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime } = 0
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{} y y^{\prime \prime }-3 {y^{\prime }}^{2} = 0
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{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
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{} \left (x^{2}+1\right ) y^{\prime \prime }+2 \left (1+y^{\prime }\right ) x = 0
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{} \left (1+y\right ) y^{\prime \prime } = 3 {y^{\prime }}^{2}
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{} y^{\prime \prime } = {\mathrm e}^{y} y^{\prime }
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{} y^{\prime \prime } = 2 y y^{\prime }
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{} 2 y^{\prime \prime } = {\mathrm e}^{y}
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{} x^{2} y^{\prime \prime }+x y^{\prime } = 1
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{} x y^{\prime \prime }-y^{\prime } = x^{2}
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{} y y^{\prime }-2 x {y^{\prime }}^{2}+x y y^{\prime \prime } = 0
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{} x y y^{\prime \prime }+x {y^{\prime }}^{2}-y y^{\prime } = 0
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{} x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+\left (1+y\right ) y^{\prime } = 0
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{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
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