| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y y^{\prime \prime } = {y^{\prime }}^{2}
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{} 3 y y^{\prime \prime } = 2 {y^{\prime }}^{2}
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{} \sin \left (y\right ) y^{\prime \prime }+\cos \left (y\right ) {y^{\prime }}^{2} = 0
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{} y y^{\prime \prime }+{y^{\prime }}^{2} = 2 y y^{\prime }
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{} y^{2} y^{\prime \prime }+y^{\prime \prime }+2 y {y^{\prime }}^{2} = 0
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{} y^{\prime \prime } = 4 x \sqrt {y^{\prime }}
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{} x y^{\prime \prime } = -y^{\prime }+{y^{\prime }}^{2}
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{} y y^{\prime \prime }-{y^{\prime }}^{2} = y^{\prime }
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{} y y^{\prime \prime } = 2 {y^{\prime }}^{2}
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{} \left (y-3\right ) y^{\prime \prime } = {y^{\prime }}^{2}
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{} y^{\prime \prime } = y^{\prime } \left (y^{\prime }-2\right )
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{} 3 y y^{\prime \prime } = 2 {y^{\prime }}^{2}
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{} y y^{\prime \prime }+2 {y^{\prime }}^{2} = 3 y y^{\prime }
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{} y^{\prime \prime } = -{\mathrm e}^{-y} y^{\prime }
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{} y^{\prime \prime } = -2 x {y^{\prime }}^{2}
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| \[
{} y^{\prime \prime } = -2 x {y^{\prime }}^{2}
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{} y^{\prime \prime } = -2 x {y^{\prime }}^{2}
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{} y^{\prime \prime } = -2 x {y^{\prime }}^{2}
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{} y^{\prime \prime } = 2 y y^{\prime }
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| \[
{} y^{\prime \prime } = 2 y y^{\prime }
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| \[
{} y^{\prime \prime } = 2 y y^{\prime }
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{} y^{\prime \prime } = 2 y y^{\prime }
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| \[
{} y^{\prime \prime }+x^{2} y^{\prime }+4 y = y^{3}
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| \[
{} \left (1+y\right ) y^{\prime \prime } = {y^{\prime }}^{3}
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{} y^{\prime \prime } = {y^{\prime }}^{2}
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{} x y^{\prime \prime }-y^{\prime } = -3 x {y^{\prime }}^{3}
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{} {y^{\prime \prime }}^{2}-5 y^{\prime \prime } y^{\prime }+4 y^{2} = 0
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{} {y^{\prime \prime }}^{2}-2 y^{\prime \prime } y^{\prime }+y^{2} = 0
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{} 2 y y^{\prime \prime }+y^{2} = {y^{\prime }}^{2}
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| \[
{} y^{\prime \prime } = {y^{\prime }}^{2}
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{} y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
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{} 2 y^{\prime \prime } = \frac {y^{\prime }}{x}+\frac {x^{2}}{y^{\prime }}
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| \[
{} y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
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{} y^{\prime \prime } = {y^{\prime }}^{2}
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| \[
{} y^{\prime \prime } = \sqrt {1-{y^{\prime }}^{2}}
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| \[
{} y^{\prime \prime } = \sqrt {1+y^{\prime }}
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| \[
{} y^{\prime \prime } = y^{\prime } \ln \left (y^{\prime }\right )
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| \[
{} y^{\prime \prime } = y^{\prime } \left (1+y^{\prime }\right )
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{} 3 y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
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{} y y^{\prime \prime } = {y^{\prime }}^{2}
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{} y^{\prime \prime } = 2 y y^{\prime }
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{} 3 y^{\prime } y^{\prime \prime } = 2 y
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{} 2 y^{\prime \prime } = 3 y^{2}
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| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 0
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| \[
{} y y^{\prime \prime } = {y^{\prime }}^{2}+y^{\prime }
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{} y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} y^{\prime }
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{} y^{\prime \prime } = {\mathrm e}^{2 y}
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| \[
{} 2 y y^{\prime \prime }-3 {y^{\prime }}^{2} = 4 y^{2}
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| \[
{} x^{\prime \prime }+{x^{\prime }}^{2}+x = 0
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| \[
{} x^{\prime \prime }-2 {x^{\prime }}^{2}+x^{\prime }-2 x = 0
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| \[
{} x^{\prime \prime }-x \,{\mathrm e}^{x^{\prime }} = 0
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| \[
{} x^{\prime \prime }+{\mathrm e}^{-x^{\prime }}-x = 0
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| \[
{} x^{\prime \prime }+x {x^{\prime }}^{2} = 0
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| \[
{} x^{\prime \prime }+\left (x+2\right ) x^{\prime } = 0
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| \[
{} x^{\prime \prime }-x^{\prime }+x-x^{2} = 0
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| \[
{} y^{\prime \prime }+y^{\prime }+y+y^{3} = 0
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| \[
{} y^{\prime \prime }+\mu \left (1-y^{2}\right ) y^{\prime }+y = 0
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{} y y^{\prime \prime }+{y^{\prime }}^{2} = 0
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| \[
{} y^{\prime \prime } = \frac {1}{\sqrt {y}}
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{} y y^{\prime \prime }+{y^{\prime }}^{2} = \ln \left (y\right ) y^{2}
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| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = 0
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| \[
{} x y y^{\prime \prime }+x {y^{\prime }}^{2}-y y^{\prime } = 0
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| \[
{} n \,x^{3} y^{\prime \prime } = \left (y-x y^{\prime }\right )^{2}
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{} y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }-x y^{2} = 0
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{} y y^{\prime \prime }-{y^{\prime }}^{2}-{y^{\prime }}^{4} = 0
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| \[
{} a^{2} y^{\prime \prime } = 2 x \sqrt {1+{y^{\prime }}^{2}}
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| \[
{} x^{2} y y^{\prime \prime }+x^{2} {y^{\prime }}^{2}-5 y y^{\prime } x = 4 y^{2}
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{} \left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime } = 0
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{} {y^{\prime \prime }}^{2}+2 x y^{\prime \prime }-y^{\prime } = 0
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{} {y^{\prime \prime }}^{2}-2 x y^{\prime \prime }-y^{\prime } = 0
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{} y^{\prime \prime }+2 y^{\prime }+y^{2} = 0
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{} y y^{\prime \prime }+{y^{\prime }}^{2} = 0
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| \[
{} x 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}
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{} y y^{\prime \prime }+{y^{\prime }}^{2}-2 y y^{\prime } = 0
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| \[
{} y^{\prime \prime }+2 x {y^{\prime }}^{2} = 0
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| \[
{} x^{2} y^{\prime \prime } = \left (3 x -2 y^{\prime }\right ) y^{\prime }
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{} y^{2} y^{\prime \prime }+{y^{\prime }}^{3} = 0
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| \[
{} {y^{\prime }}^{2}+x^{2} y^{\prime \prime } = 0
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{} y^{\prime \prime } = 2 {y^{\prime }}^{3} y
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{} y^{\prime \prime }+{y^{\prime }}^{2} = 0
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| \[
{} x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5} = 0
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| \[
{} x^{2} y^{\prime \prime }-\frac {x^{2} {y^{\prime }}^{2}}{2 y}+4 x y^{\prime }+4 y = 0
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| \[
{} v^{\prime \prime } = \left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}}
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{} \sqrt {y^{\prime }+y} = \left (y^{\prime \prime }+2 x \right )^{{1}/{4}}
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{} y^{\prime \prime } = \frac {m \sqrt {1+{y^{\prime }}^{2}}}{k}
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| \[
{} \phi ^{\prime \prime } = \frac {4 \pi n c}{\sqrt {v_{0}^{2}+\frac {2 e \left (\phi -V_{0} \right )}{m}}}
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| \[
{} y^{\prime \prime } = c \left (1+{y^{\prime }}^{2}\right )
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{} y^{\prime \prime } = c \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
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| \[
{} y^{\prime \prime }-2 y y^{\prime } = 0
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| \[
{} y^{\prime \prime }-{y^{\prime }}^{2}-{y^{\prime }}^{3} y = 0
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| \[
{} \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = r y^{\prime \prime }
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| \[
{} \left (1+y^{2}\right ) y^{\prime \prime }-2 y {y^{\prime }}^{2}-2 \left (1+y^{2}\right ) y^{\prime } = y^{2} \left (1+y^{2}\right )
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{} y^{\prime \prime } = \frac {1}{y^{2}}
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| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = 0
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