| # | ODE | Mathematica | Maple | Sympy |
| \[
{} {y^{\prime }}^{3}+y y^{\prime \prime } = 0
\]
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| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 0
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| \[
{} y y^{\prime \prime } = {y^{\prime }}^{2} \left (1-\cos \left (y\right ) y^{\prime }+y y^{\prime } \sin \left (y\right )\right )
\]
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{} y y^{\prime \prime }-{y^{\prime }}^{2} = \ln \left (y\right ) y^{2}
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| \[
{} 2 \left (1+y\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}+y^{2}+2 y = 0
\]
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| \[
{} u^{\prime \prime }+u^{\prime }+u = \cos \left (r +u\right )
\]
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| \[
{} y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
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| \[
{} R^{\prime \prime } = -\frac {k}{R^{2}}
\]
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| \[
{} x^{\prime \prime }-\left (1-\frac {{x^{\prime }}^{2}}{3}\right ) x^{\prime }+x = 0
\]
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| \[
{} 2 y^{\prime \prime }-3 y^{2} = 0
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| \[
{} y^{\prime \prime } = 2 {y^{\prime }}^{3} y
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| \[
{} x^{2} y y^{\prime \prime } = x^{2} {y^{\prime }}^{2}-y^{2}
\]
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| \[
{} x x^{\prime \prime }-{x^{\prime }}^{2} = 0
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| \[
{} y y^{\prime \prime }-y^{2} y^{\prime }-{y^{\prime }}^{2} = 0
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| \[
{} y y^{\prime \prime }+4 {y^{\prime }}^{2} = 0
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| \[
{} y^{\prime \prime } = y y^{\prime }
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| \[
{} y^{\prime \prime } = -\frac {1}{2 {y^{\prime }}^{2}}
\]
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| \[
{} y^{\prime \prime }+\sin \left (y\right ) = 0
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| \[
{} y^{\prime \prime }+\sin \left (y\right ) = 0
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| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 0
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| \[
{} x y y^{\prime \prime } = {y^{\prime }}^{3}+y^{\prime }
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| \[
{} x^{2} y^{\prime \prime } = 2 x y^{\prime }+{y^{\prime }}^{2}
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| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = 0
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| \[
{} \left (x^{2}+2 y^{\prime }\right ) y^{\prime \prime }+2 x y^{\prime } = 0
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| \[
{} y y^{\prime \prime } = y^{2} y^{\prime }+{y^{\prime }}^{2}
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| \[
{} y^{\prime \prime } = {\mathrm e}^{y} y^{\prime }
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| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = 0
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| \[
{} x y^{\prime \prime } = y^{\prime }-2 {y^{\prime }}^{3}
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| \[
{} y y^{\prime \prime }+y^{\prime } = 0
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| \[
{} y^{\prime \prime }+\sin \left (y\right ) = 0
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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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| \[
{} 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 }}^{3}+y y^{\prime \prime } = 0
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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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| \[
{} 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 } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
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| \[
{} y y^{\prime \prime } = {y^{\prime }}^{2} \left (1-y^{\prime } \sin \left (y\right )-\cos \left (y\right ) y y^{\prime }\right )
\]
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| \[
{} \left (1+y^{2}\right ) y^{\prime \prime }+{y^{\prime }}^{3}+y^{\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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| \[
{} x^{2} y^{\prime \prime } = y^{\prime } \left (2 x -y^{\prime }\right )
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| \[
{} x^{2} y^{\prime \prime } = \left (3 x -2 y^{\prime }\right ) y^{\prime }
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| \[
{} x y^{\prime \prime } = y^{\prime } \left (2-3 x y^{\prime }\right )
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| \[
{} x^{4} y^{\prime \prime } = y^{\prime } \left (y^{\prime }+x^{3}\right )
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| \[
{} y^{\prime }-x y^{\prime \prime }+{y^{\prime \prime }}^{2} = 0
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| \[
{} {y^{\prime \prime }}^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right )
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| \[
{} y^{\prime \prime } = \frac {1}{y}-\frac {x y^{\prime }}{y^{2}}
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+x {y^{\prime }}^{2} = 1
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{} \left (x^{2}+1\right ) y^{\prime \prime }+y {y^{\prime }}^{2} = 0
\]
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{} \left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2} = 0
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| \[
{} y^{\prime \prime }+{y^{\prime }}^{2} \sin \left (y\right ) = 0
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{} \left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{3} = 0
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| \[
{} y^{\prime \prime } = A y^{{2}/{3}}
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| \[
{} y^{\prime \prime }+{\mathrm e}^{y} = 0
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| \[
{} {y^{\prime \prime }}^{2}+y^{\prime } = 0
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| \[
{} y^{\prime \prime }+{y^{\prime }}^{2} = 0
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| \[
{} {y^{\prime \prime }}^{2}+y^{\prime }+y = 0
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| \[
{} y^{\prime \prime }+{y^{\prime }}^{2}+y = 0
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| \[
{} y {y^{\prime \prime }}^{2}+y^{\prime } = 0
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{} y {y^{\prime \prime }}^{2}+{y^{\prime }}^{3} = 0
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| \[
{} y^{2} {y^{\prime \prime }}^{2}+y^{\prime } = 0
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| \[
{} y {y^{\prime \prime }}^{4}+{y^{\prime }}^{2} = 0
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| \[
{} y^{3} {y^{\prime \prime }}^{2}+y y^{\prime } = 0
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| \[
{} {y^{\prime }}^{3}+y y^{\prime \prime } = 0
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| \[
{} y {y^{\prime \prime }}^{3}+y^{3} y^{\prime } = 0
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| \[
{} y {y^{\prime \prime }}^{3}+y^{3} {y^{\prime }}^{5} = 0
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| \[
{} y^{\prime \prime }+x y^{\prime }+y {y^{\prime }}^{2} = 0
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| \[
{} y^{\prime \prime }+y^{\prime } \sin \left (x \right )+y {y^{\prime }}^{2} = 0
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{} y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y^{2} {y^{\prime }}^{2} = 0
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| \[
{} y^{\prime \prime }+\left (\sin \left (x \right )+2 x \right ) y^{\prime }+\cos \left (y\right ) y {y^{\prime }}^{2} = 0
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| \[
{} y^{\prime } y^{\prime \prime }+y^{2} = 0
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| \[
{} y^{\prime } y^{\prime \prime }+y^{n} = 0
\]
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| \[
{} y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (y^{2}+3\right ) {y^{\prime }}^{2} = 0
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{} y^{\prime \prime }+x y^{\prime }+y {y^{\prime }}^{2} = 0
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{} y^{\prime \prime }+y^{\prime } \sin \left (x \right )+{y^{\prime }}^{2} = 0
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{} 3 y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+{y^{\prime }}^{2} \sin \left (y\right ) = 0
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| \[
{} 10 y^{\prime \prime }+x^{2} y^{\prime }+\frac {3 {y^{\prime }}^{2}}{y} = 0
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{} 10 y^{\prime \prime }+\left ({\mathrm e}^{x}+3 x \right ) y^{\prime }+\frac {3 \,{\mathrm e}^{y} {y^{\prime }}^{2}}{\sin \left (y\right )} = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2} = 0
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| \[
{} y^{\prime \prime }-y^{2} = 0
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| \[
{} y^{\prime \prime }-6 y^{2} = 0
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{} y^{\prime \prime }-6 y^{2}+4 y = 0
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| \[
{} y^{\prime \prime }-a y^{3} = 0
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| \[
{} y^{\prime \prime }+a \,x^{r} y^{2} = 0
\]
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| \[
{} y^{\prime \prime }+6 a^{10} y^{11}-y = 0
\]
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| \[
{} y^{\prime \prime }-\frac {1}{\left (a y^{2}+b x y+c \,x^{2}+\alpha y+\beta x +\gamma \right )^{{3}/{2}}} = 0
\]
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