| # | ODE | Mathematica | Maple | Sympy |
| \[
{} -b y a +\left (c -\left (1+a +b \right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x^{3}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 x y^{\prime }-8 y = 4 \ln \left (x \right )
\]
|
✓ |
✗ |
✗ |
|
| \[
{} x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+x y^{\prime }-y = -\ln \left (x \right )
\]
|
✓ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [w^{\prime }\left (t \right )+y \left (t \right ) = \sin \left (t \right ), y^{\prime }\left (t \right )-z \left (t \right ) = {\mathrm e}^{t}, w \left (t \right )+y \left (t \right )+z^{\prime }\left (t \right ) = 1]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+4 y = 0
\]
|
✓ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime } \cos \left (y\right )+\left (\cos \left (y\right )-y^{\prime } \sin \left (y\right )\right ) y^{\prime }-2 x y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 2 x^{4} y y^{\prime }+y^{4} = 4 x^{6}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = x y^{\prime \prime }+{y^{\prime \prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y y^{\prime \prime } = {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = {\mathrm e}^{y} y^{\prime }
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\frac {2 {y^{\prime }}^{2}}{y}-y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 1+{y^{\prime }}^{2}+y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y = 2 x y^{\prime }-{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y = 2 x +y^{\prime }-\frac {{y^{\prime }}^{3}}{3}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x {y^{\prime }}^{2}-3 y y^{\prime }+9 x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } \left (y^{\prime }+y\right ) = x \left (x +y\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y {y^{\prime }}^{2}-\left (x y+x +y^{2}\right ) y^{\prime }+x^{2}+x y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+4 y \left (t \right )-y \left (t \right )^{2}, y^{\prime }\left (t \right ) = 6 x \left (t \right )-y \left (t \right )+2 x \left (t \right ) y \left (t \right )]
\]
|
✗ |
✗ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = \sin \left (x \left (t \right )\right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = \sin \left (2 x \left (t \right )\right )-5 y \left (t \right )]
\]
|
✗ |
✗ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = 8 x \left (t \right )-y \left (t \right )^{2}, y^{\prime }\left (t \right ) = 6 x \left (t \right )^{2}-6 y \left (t \right )]
\]
|
✗ |
✗ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )^{2}-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )^{3}-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\]
|
✗ |
✗ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 3 y \left (t \right )^{2}-x \left (t \right )^{2}]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )^{2}, y^{\prime }\left (t \right ) = x \left (t \right )^{2}-y \left (t \right )]
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime } = 4 x^{3}-4 x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime }+\sin \left (x\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime } = x^{2}-4 x+\lambda
\]
|
✓ |
✓ |
✗ |
|
| \[
{} {\mathrm e}^{x} \sec \left (y\right )+\left ({\mathrm e}^{x}+1\right ) \sec \left (y\right ) \tan \left (y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {y}{x}-\csc \left (\frac {y}{x}\right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a x -b y+\left (b x -a y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 x^{2}+5 x y^{2}+\left (5 x^{2} y-2 y^{4}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} a +2 b x y+c y^{2}+\left (b \,x^{2}+2 c x y+y^{2}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 x \sin \left (y\right )+2 x +3 y \cos \left (x \right )+\left (x^{2} \cos \left (y\right )+3 \sin \left (x \right )\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y \,{\mathrm e}^{2 x}-3 x \,{\mathrm e}^{2 y}+\left (\frac {{\mathrm e}^{2 x}}{2}-3 x^{2} {\mathrm e}^{2 y}-{\mathrm e}^{y}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime }-y = x^{2} \sqrt {x^{2}-y^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y = \left (2 x^{2} y^{3}-x \right ) y^{\prime }
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{3} \left (y y^{\prime }+x \right ) = \left (x^{2}+y^{2}\right )^{3} y^{\prime }
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 3 x^{2}-2 x y+\left (4 y^{3}-x^{2}\right ) y^{\prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} 2 x -y+1+\left (x -2 y-1\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a x y-b +\left (c x y-d \right ) x y^{\prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 2 {y^{\prime }}^{3}+3 {y^{\prime }}^{2} = x +y
\]
|
✗ |
✓ |
✗ |
|
| \[
{} 2 a \,x^{3} y-a \,x^{2} y^{\prime }+c {y^{\prime }}^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{2}-2 y y^{\prime } x +x^{2} {y^{\prime }}^{2}-{y^{\prime }}^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 x +y y^{\prime } \left (4 {y^{\prime }}^{2}+6\right ) = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} 2 y^{\prime \prime \prime }+x y^{\prime \prime }+2 y^{\prime }+x y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (2 x -1\right ) y^{\prime \prime }-3 y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-n^{2}+x^{2}\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime \prime }\left (t \right ) = 1, x^{\prime }\left (t \right )+x \left (t \right )+y^{\prime \prime }\left (t \right )-9 y \left (t \right )+z^{\prime }\left (t \right )+z \left (t \right ) = 0, 5 x \left (t \right )+z^{\prime \prime }\left (t \right )-4 z \left (t \right ) = 2]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 x +\frac {1}{y}+\left (\frac {1}{y}-\frac {x}{y^{2}}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{3}+3\right ) y^{\prime }+2 x y+5 x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} t y^{\prime \prime }+t^{2} y^{\prime }-\sin \left (t \right ) \sqrt {t} = t^{2}-t +1
\]
|
✓ |
✓ |
✗ |
|
| \[
{} s^{2} t^{\prime \prime }+s t t^{\prime } = s
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 5 {b^{\prime \prime \prime \prime }}^{5}+7 {b^{\prime }}^{10}+b^{7}-b^{5} = p
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime \prime } = 1+y^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} {y^{\prime \prime }}^{2}-3 y y^{\prime }+x y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{4} y^{\prime \prime \prime \prime }+x y^{\prime \prime \prime } = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime \prime \prime }+x y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-x y^{\prime }+\sin \left (y\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} {r^{\prime \prime }}^{2}+r^{\prime \prime }+y r^{\prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} {y^{\prime \prime }}^{{3}/{2}}+y = x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} {b^{\prime }}^{7} = 3 p
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+4 y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = \sin \left (x \right ) y+{\mathrm e}^{x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = x \sin \left (y\right )+{\mathrm e}^{x}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = x +y^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 1+x y+y y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {2 x y}{-x^{2}+y^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {y}{x +\sqrt {x y}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {y^{2}}{x y+\left (x y^{2}\right )^{{1}/{3}}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {x^{4}+3 x^{2} y^{2}+y^{4}}{x^{3} y}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x +\sin \left (y\right )+\left (x \cos \left (y\right )-2 y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {2+y \,{\mathrm e}^{x y}}{2 y-x \,{\mathrm e}^{x y}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y+2 x y^{3}+\left (1+3 x^{2} y^{2}+x \right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y-x y^{2}+\left (x^{2} y^{2}+x \right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{2} x^{3}-y+\left (x^{2} y^{4}-x \right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 x y^{\prime \prime }+x^{2} y^{\prime }-\sin \left (x \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime \prime \prime }+x y^{\prime }+y = x^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }+\left (1+x \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime \prime \prime }+x^{2} y^{\prime \prime \prime }+x y^{\prime \prime }-{\mathrm e}^{x} y^{\prime }+2 y = x^{2}+x +1
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+2 x y^{\prime }+y = 4 x y^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime }+y^{\prime \prime } = x^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime \prime }+\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime }+y = 5 \sin \left (x \right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime }-\frac {2 y}{x} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\frac {y}{x} = x^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+2 y^{\prime }+x y = 0
\]
|
✓ |
✗ |
✗ |
|
| \[
{} x^{3} y^{\prime \prime }+y = 0
\]
|
✓ |
✗ |
✗ |
|
| \[
{} x^{3} y^{\prime \prime }+x y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (1+x \right )^{3} y^{\prime \prime }+\left (x^{2}-1\right ) \left (1+x \right ) y^{\prime }+\left (x -1\right ) y = 0
\]
|
✓ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+x y = 2
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2}+4\right ) y^{\prime \prime }+x y = x +2
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (x -1\right ) y = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2}+4\right ) y^{\prime \prime }+y = x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\left (x -1\right ) y^{\prime } = x^{2}-2 x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x y^{\prime } = {\mathrm e}^{-x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-2 x y = x^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -b y a +\left (c -\left (1+a +b \right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+\left (3 x -1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|