| # | ODE | Mathematica | Maple | Sympy |
| \[
{} \left (2 A x y+B \,x^{2}+a y+b x +c \right ) y^{\prime } = A y^{2}+k \left (A k +B \right ) x^{2}+b y+a \,k^{2} x +s
\]
|
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|
| \[
{} \left (\left (x +c \right ) y+\left (n +1\right ) x^{2}-a \left (2 n +1\right ) x +a^{2} n \right ) y^{\prime } = \frac {2 n y^{2}}{3 n -1}+2 x y
\]
|
✗ |
✗ |
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|
| \[
{} \left (\left (a_{2} x^{2}+a_{1} x +a_{0} \right ) y+b_{2} x^{2}+b_{1} x +b_{0} \right ) y^{\prime } = c_{2} y^{2}+c_{1} y+c_{0}
\]
|
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|
| \[
{} \left (\left (12 a^{2} x^{2}-7 a x +1\right ) y+4 c \,x^{2}-5 b x \right ) y^{\prime } = -2 x \left (3 a^{2} y^{2}+2 c y+3 b^{2}\right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x \left (2 a x y+b \right ) y^{\prime } = -4 a \,x^{2} y^{2}-3 b x y+c \,x^{2}+k
\]
|
✗ |
✗ |
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|
| \[
{} y y^{\prime } = -n y^{2}+a \left (2 n +1\right ) {\mathrm e}^{x} y+b y-a^{2} n \,{\mathrm e}^{2 x}-a b \,{\mathrm e}^{x}+c
\]
|
✗ |
✗ |
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|
| \[
{} y^{\prime } = a x y^{3}+2 a b \,x^{2} y^{2}-b -2 a \,b^{3} x^{4}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 9 y^{\prime } = -x^{m} \left (a \,x^{1-m}+b \right )^{2 \lambda +1} y^{3}-x^{-2 m} \left (9 a +2+9 b m \,x^{m -1}\right ) \left (a \,x^{1-m}+b \right )^{-\lambda -2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = -\left (a x +b \,x^{m}\right ) y^{3}+y^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = \frac {y^{3}}{\sqrt {x^{2} a +b x +c}}+y^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (-c \,x^{2 n}+a \,x^{n +1}+b \,x^{n}+n \,x^{n -1}\right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+a \,x^{n} y^{\prime }-b \left (a \,x^{m +n}+b \,x^{2 m}+m \,x^{m -1}\right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}+b -c \right ) y = 0
\]
|
✗ |
✗ |
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|
| \[
{} y^{\prime \prime }+\left (a b \,x^{n}+b \,x^{n -1}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{n}+1\right ) y = 0
\]
|
✗ |
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✗ |
|
| \[
{} y^{\prime \prime }+\left (a b \,x^{n}+2 b \,x^{n -1}-a^{2} x \right ) y^{\prime }+a \left (a b \,x^{n}+b \,x^{n -1}-a^{2} x \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+c \left (a \,x^{n}+b \,x^{m}-c \right ) y = 0
\]
|
✗ |
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|
| \[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a b \,x^{m +n}+b \left (1+m \right ) x^{m -1}-a \,x^{n -1}\right ) y = 0
\]
|
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|
| \[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (a b \,x^{m +n}+b c \,x^{m}+a n \,x^{n -1}\right ) y = 0
\]
|
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|
| \[
{} x y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (a b \,x^{n}-a \,x^{n -1}-b^{2} x +2 b \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}-c x +b \right ) y = 0
\]
|
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|
| \[
{} x y^{\prime \prime }+\left (a b \,x^{n}+b -3 n +1\right ) y^{\prime }+a^{2} n \left (b -n \right ) x^{-1+2 n} y = 0
\]
|
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✗ |
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|
| \[
{} x y^{\prime \prime }+\left (a \,x^{n}+b x \right ) y^{\prime }+\left (a b \,x^{n}+a n \,x^{n -1}-b \right ) y = 0
\]
|
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|
| \[
{} x y^{\prime \prime }+\left (a b \,x^{n}+b \,x^{n -1}+a x -1\right ) y^{\prime }+a^{2} b \,x^{n} y = 0
\]
|
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|
| \[
{} x y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (c -1\right ) \left (a \,x^{n -1}+b \,x^{m -1}\right ) y = 0
\]
|
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|
| \[
{} x y^{\prime \prime }+\left (a b \,x^{m +n}+a n \,x^{n}+b \,x^{m}+1-2 n \right ) y^{\prime }+a^{2} b n \,x^{2 n +m -1} y = 0
\]
|
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|
| \[
{} x^{2} y^{\prime \prime }+\left (a \,x^{2 n} \left (b \,x^{n}+c \right )^{m}+\frac {1}{4}-\frac {n^{2}}{4}\right ) y = 0
\]
|
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|
| \[
{} x^{2} y^{\prime \prime }+a \,x^{n} y^{\prime }-\left (a b \,x^{n}+a c \,x^{n -1}+b^{2} x^{2}+2 b c x +c^{2}-c \right ) y = 0
\]
|
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|
| \[
{} x^{2} y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (a b \,x^{n +2 m}-b^{2} x^{4 m +2}+a m \,x^{n -1}-m^{2}-m \right ) y = 0
\]
|
✗ |
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|
| \[
{} x^{2} y^{\prime \prime }+\left (a \,x^{n +2}+b \,x^{2}+c \right ) y^{\prime }+\left (a n \,x^{n +1}+a c \,x^{n}+b c \right ) y = 0
\]
|
✗ |
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✗ |
|
| \[
{} x^{3} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime } x -\left (a \,x^{n}-a b \,x^{n -1}+b \right ) y = 0
\]
|
✗ |
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|
| \[
{} \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\left (\alpha \gamma +\beta \right ) x +\beta \lambda \right ) y^{\prime }-\left (x \alpha +\beta \right ) y = 0
\]
|
✗ |
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|
| \[
{} x^{4} y^{\prime \prime }+a \,x^{n} y^{\prime }-\left (a \,x^{n -1}+a b \,x^{n -2}+b^{2}\right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (x^{2}+a \right )^{2} y^{\prime \prime }+b \,x^{n} \left (x^{2}+a \right ) y^{\prime }-\left (b \,x^{n +1}+a \right ) y = 0
\]
|
✗ |
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✗ |
|
| \[
{} \left (x^{2}+a \right )^{2} y^{\prime \prime }+b \,x^{n} \left (x^{2}+a \right ) y^{\prime }-m \left (b \,x^{n +1}+\left (m -1\right ) x^{2}+a \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{n} y^{\prime \prime }+c \left (a x +b \right )^{n -4} y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{n} y^{\prime \prime }+a x y^{\prime }-\left (b^{2} x^{n}+2 b \,x^{n -1}+a b x +a \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{n} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{n}+b \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{n} y^{\prime \prime }+\left (a \,x^{n}-x^{n -1}+a b x +b \right ) y^{\prime }+y a^{2} b x = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{n} y^{\prime \prime }+\left (a \,x^{m +n}+1\right ) y^{\prime }+a \,x^{m} \left (1+m \,x^{n -1}\right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (a \,x^{n}+b \right ) y^{\prime \prime }+\left (c \,x^{n}+d \right ) y^{\prime }+\lambda \left (\left (-a \lambda +c \right ) x^{n}+d -b \lambda \right ) y = 0
\]
|
✗ |
✗ |
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|
| \[
{} \left (x^{n}+a \right )^{2} y^{\prime \prime }+b \,x^{m} \left (x^{n}+a \right ) y^{\prime }-x^{n -2} \left (b \,x^{1+m}+a n -a \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (a \,x^{n}+b \right )^{2} y^{\prime \prime }+c \,x^{m} \left (a \,x^{n}+b \right ) y^{\prime }+\left (c \,x^{m}-a n \,x^{n -1}-1\right ) y = 0
\]
|
✗ |
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✗ |
|
| \[
{} \left (a \,x^{n +1}+b \,x^{n}+c \right )^{2} y^{\prime \prime }+\left (\alpha \,x^{n}+\beta \,x^{n -1}+\gamma \right ) y^{\prime }+\left (n \left (-a n -a +\alpha \right ) x^{n -1}+\left (n -1\right ) \left (-b n +\beta \right ) x^{n -2}\right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 2 \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+a n \,x^{n -1} b m \,x^{m -1} y^{\prime }+y d = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{x \mu }\right ) y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{x \mu }+\lambda \right ) y = 0
\]
|
✗ |
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✗ |
|
| \[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{x \mu }+c \right ) y^{\prime }+\left (a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x}+{\mathrm e}^{\lambda x} a c +b \mu \,{\mathrm e}^{x \mu }\right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (a \,{\mathrm e}^{\left (\lambda +\mu \right ) x}+a \lambda \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{x \mu }-2 \lambda \right ) y^{\prime }+a^{2} b \lambda \,{\mathrm e}^{\left (\mu +2 \lambda \right ) x} y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{4} x^{3}+x^{2} y^{3}+x y^{2}+y+\left (y^{3} x^{4}-y^{2} x^{3}-x^{3} y+x \right ) y^{\prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (x -y^{\prime }-y\right )^{2} = x^{2} \left (2 x y-x^{2} y^{\prime }\right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{2} \left (-x^{3}+1\right ) y^{\prime \prime }-x^{3} y^{\prime }-2 y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} {x^{\prime }}^{2}+t x = \sqrt {t +1}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+y = 0
\]
|
✗ |
✗ |
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|
| \[
{} 3 x^{2} y+2-\left (x^{3}+y\right ) y^{\prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (2 t +1\right ) x^{\prime \prime }+t^{3} x^{\prime }+x = 0
\]
|
✗ |
✗ |
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|
| \[
{} f \left (t \right ) x^{\prime \prime }+x g \left (t \right ) = 0
\]
|
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|
| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-4 y \left (t \right )-x \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+4 y \left (t \right )-y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )]
\]
|
✗ |
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|
| \[
{} \left [x^{\prime }\left (t \right ) = y \left (t \right )+\frac {x \left (t \right ) \left (1-x \left (t \right )^{2}-y \left (t \right )^{2}\right )}{\sqrt {x \left (t \right )^{2}+y \left (t \right )^{2}}}, y^{\prime }\left (t \right ) = -x \left (t \right )+\frac {y \left (t \right ) \left (1-x \left (t \right )^{2}-y \left (t \right )^{2}\right )}{\sqrt {x \left (t \right )^{2}+y \left (t \right )^{2}}}\right ]
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{\prime \prime }+x^{4} x^{\prime }-x^{\prime }+x = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{\prime \prime }+x^{\prime }+{x^{\prime }}^{3}+x = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{\prime \prime }+\left (x^{4}+x^{2}\right ) x^{\prime }+x^{3}+x = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{\prime \prime }+\left (1+x^{2}\right ) x^{\prime }+x^{3} = 0
\]
|
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|
| \[
{} \left (\cos \left (t \right ) t -\sin \left (t \right )\right ) x^{\prime \prime }-x^{\prime } t \sin \left (t \right )-x \sin \left (t \right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = x y^{3}+x^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = \sin \left (x y\right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = \ln \left (x y\right )
\]
|
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✗ |
|
| \[
{} y^{\prime \prime }+y y^{\prime \prime \prime \prime } = 1
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime \prime }+x y^{\prime \prime }-y^{2} = \sin \left (x \right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} {y^{\prime }}^{2}+x y {y^{\prime }}^{2} = \ln \left (x \right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \sin \left (y^{\prime \prime }\right )+y y^{\prime \prime \prime \prime } = 1
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \sinh \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime } = x y
\]
|
✗ |
✗ |
✗ |
|
| \[
{} {y^{\prime \prime \prime }}^{2}+\sqrt {y} = \sin \left (x \right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (x -3\right ) y^{\prime \prime }+y \ln \left (x \right ) = x^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x y^{\prime \prime }+2 x^{2} y^{\prime }+\sin \left (x \right ) y = \sinh \left (x \right )
\]
|
✗ |
✗ |
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|
| \[
{} \sin \left (x \right ) y^{\prime \prime }+x y^{\prime }+7 y = 1
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \ln \left (x^{2}+1\right ) y^{\prime \prime }+\frac {4 x y^{\prime }}{x^{2}+1}+\frac {\left (-x^{2}+1\right ) y}{\left (x^{2}+1\right )^{2}} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x y^{\prime \prime }+\left (6 x y^{2}+1\right ) y^{\prime }+2 y^{3}+1 = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+\frac {\left (x -1\right ) y^{\prime }}{x}+\frac {y}{x^{3}} = \frac {{\mathrm e}^{-\frac {1}{x}}}{x^{3}}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} t^{2} y^{\prime \prime }-6 t y^{\prime }+y \sin \left (2 t \right ) = \ln \left (t \right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+t y^{\prime }-y \ln \left (t \right ) = \cos \left (2 t \right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{\prime \prime }+x^{\prime }+x-x^{3} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{\prime \prime }+x^{\prime }+x+x^{3} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = y^{3}+x^{3}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = \frac {1}{\sqrt {15-x^{2}-y^{2}}}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (x^{2}-4\right ) y^{\prime \prime }+y \ln \left (x \right ) = x \,{\mathrm e}^{x}
\]
|
✗ |
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|
| \[
{} \left [y_{1}^{\prime }\left (x \right ) = \sin \left (x \right ) y_{1} \left (x \right )+\sqrt {x}\, y_{2} \left (x \right )+\ln \left (x \right ), y_{2}^{\prime }\left (x \right ) = \tan \left (x \right ) y_{1} \left (x \right )-{\mathrm e}^{x} y_{2} \left (x \right )+1\right ]
\]
|
✗ |
✗ |
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|
| \[
{} \left [y_{1}^{\prime }\left (x \right ) = \sin \left (x \right ) y_{1} \left (x \right )+\sqrt {x}\, y_{2} \left (x \right )+\ln \left (x \right ), y_{2}^{\prime }\left (x \right ) = \tan \left (x \right ) y_{1} \left (x \right )-{\mathrm e}^{x} y_{2} \left (x \right )+1\right ]
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left [y_{1}^{\prime }\left (x \right ) = {\mathrm e}^{-x} y_{1} \left (x \right )-\sqrt {1+x}\, y_{2} \left (x \right )+x^{2}, y_{2}^{\prime }\left (x \right ) = \frac {y_{1} \left (x \right )}{\left (x -2\right )^{2}}\right ]
\]
|
✗ |
✗ |
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|
| \[
{} \left [y_{1}^{\prime }\left (x \right ) = {\mathrm e}^{-x} y_{1} \left (x \right )-\sqrt {1+x}\, y_{2} \left (x \right )+x^{2}, y_{2}^{\prime }\left (x \right ) = \frac {y_{1} \left (x \right )}{\left (x -2\right )^{2}}\right ]
\]
|
✗ |
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|
| \[
{} [y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right ) x -x^{2} y_{2} \left (x \right )+4 x, y_{2}^{\prime }\left (x \right ) = {\mathrm e}^{x} y_{1} \left (x \right )+3 \,{\mathrm e}^{-x} y_{2} \left (x \right )-\cos \left (3 x \right )]
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = 2 y^{3}+t^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = \left (y-3\right ) \left (\sin \left (y\right ) \sin \left (t \right )+\cos \left (t \right )+1\right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = \left (-1+y\right ) \left (-2+y\right ) \left (y-{\mathrm e}^{\frac {t}{2}}\right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{2} y^{\prime \prime } = 8 x^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \sin \left (x +y\right )-y y^{\prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{2} y^{\prime }+3 x^{2} y = \sin \left (x \right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+x^{2} y^{\prime }+4 y = y^{3}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime } = y
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{3} y^{\prime \prime \prime }-4 y^{\prime \prime }+10 y^{\prime }-12 y = 0
\]
|
✗ |
✗ |
✗ |
|