| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -y+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 \left (1-x \right ) y^{\prime \prime }+y^{\prime } \left (1+x \right )+\left (x -3-\left (x -1\right )^{2} {\mathrm e}^{x}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (1-2 x \right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x \left (x +3\right ) y^{\prime }+\left (x^{2}+x +1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 3 x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-\lambda y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-p^{2}+x^{2}\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -b y a +\left (c -\left (1+a +b \right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x^{3}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 x y^{\prime }-8 y = 4 \ln \left (x \right )
\]
|
✓ |
✗ |
✗ |
|
| \[
{} x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+x y^{\prime }-y = -\ln \left (x \right )
\]
|
✓ |
✗ |
✗ |
|
| \[
{} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+p y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime }-5 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime }-5 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime }-5 y = {\mathrm e}^{5 t}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y+y^{\prime } = t
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -2 y+y^{\prime } = {\mathrm e}^{5 t}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y+y^{\prime } = \sin \left (t \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime }+2 y = \cos \left (t \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime }+b y = 1
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime }+2 y = {\mathrm e}^{-t}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+4 y^{\prime }+8 y = \sin \left (t \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-t}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+2 y^{\prime }+y = t
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & t <1 \\ 2 & 1\le t \end {array}\right .
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & t <6 \\ 1 & 6\le t \end {array}\right .
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 4 t & 0\le t \le 1 \\ 4 & 1<t \end {array}\right .
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime \prime }+y^{\prime } = {\mathrm e}^{t}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+2 y = 10 \cos \left (t \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right )-6 x \left (t \right )+3 y \left (t \right ) = 8 \,{\mathrm e}^{t}, y^{\prime }\left (t \right )-2 x \left (t \right )-y \left (t \right ) = 4 \,{\mathrm e}^{t}]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y^{\prime }\left (t \right )+z \left (t \right ) = t, z^{\prime }\left (t \right )+4 y \left (t \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [w^{\prime }\left (t \right )+y \left (t \right ) = \sin \left (t \right ), y^{\prime }\left (t \right )-z \left (t \right ) = {\mathrm e}^{t}, w \left (t \right )+y \left (t \right )+z^{\prime }\left (t \right ) = 1]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+2 y^{\prime }-3 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+2 y^{\prime }-3 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 y+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 y+y^{\prime \prime } = 0
\]
|
✓ |
✗ |
✗ |
|
| \[
{} 4 y+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \sqrt {1-y^{2}}+\left (2 y+x \right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left [y^{\prime }\left (t \right ) = -\sqrt {1-y \left (t \right )^{2}}, x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )\right ]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } \cos \left (y\right )+\left (\cos \left (y\right )-y^{\prime } \sin \left (y\right )\right ) y^{\prime }-2 x y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = 8 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+12 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )+4 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-4 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+2 y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = -y \left (t \right )+z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 9 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 7 x \left (t \right )-y \left (t \right )+6 z \left (t \right ), y^{\prime }\left (t \right ) = -10 x \left (t \right )+4 y \left (t \right )-12 z \left (t \right ), z^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )-z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x \left (t \right )+y^{\prime }\left (t \right ) = \sin \left (t \right )+\cos \left (t \right ), x^{\prime }\left (t \right )+y \left (t \right ) = \cos \left (t \right )-\sin \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -5 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 6 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [2 x^{\prime }\left (t \right )-3 y^{\prime }\left (t \right ) = 2 \,{\mathrm e}^{2 t}, x^{\prime }\left (t \right )-2 y^{\prime }\left (t \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y^{\prime }\left (t \right ) = y \left (t \right )-3 z \left (t \right ), z^{\prime }\left (t \right ) = 2 y \left (t \right )-4 z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )+4 y \left (t \right )]
\]
|
✓ |
✗ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 7 x \left (t \right )-y \left (t \right )+6 z \left (t \right ), y^{\prime }\left (t \right ) = -10 x \left (t \right )+4 y \left (t \right )-12 z \left (t \right ), z^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )-z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = 3 x \left (t \right )+3 y \left (t \right )-z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )+3 z \left (t \right ), z^{\prime }\left (t \right ) = 3 y \left (t \right )+z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right )+{\mathrm e}^{t}, y^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right )+1]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )-5 t, y^{\prime }\left (t \right ) = 3 x \left (t \right )+6 y \left (t \right )-4]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )+3 \,{\mathrm e}^{2 t}, y^{\prime }\left (t \right ) = -4 x \left (t \right )+2 y \left (t \right )+t \,{\mathrm e}^{2 t}]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 x^{4} y y^{\prime }+y^{4} = 4 x^{6}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} {y^{\prime \prime }}^{2} x^{2} \left (x^{2}-1\right )-1 = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }-{y^{\prime }}^{3}-y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = x y^{\prime \prime }+{y^{\prime \prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y y^{\prime \prime } = {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = {\mathrm e}^{y} y^{\prime }
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\frac {2 {y^{\prime }}^{2}}{y}-y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 1+{y^{\prime }}^{2}+y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x = y-{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y = 2 x y^{\prime }-{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y = 2 x +y^{\prime }-\frac {{y^{\prime }}^{3}}{3}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x {y^{\prime }}^{2}-3 y y^{\prime }+9 x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } \left (y^{\prime }+y\right ) = x \left (x +y\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} {y^{\prime }}^{2}+4 y y^{\prime } x +3 y^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1 = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y {y^{\prime }}^{2}-\left (x y+x +y^{2}\right ) y^{\prime }+x^{2}+x y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} 2 {y^{\prime }}^{2}-2 y y^{\prime }-1 = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left ({y^{\prime }}^{2}-y^{2}\right ) {\mathrm e}^{y^{\prime }}-x {y^{\prime }}^{2}+x y^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-7 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-8 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+6 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+4 y \left (t \right )-y \left (t \right )^{2}, y^{\prime }\left (t \right ) = 6 x \left (t \right )-y \left (t \right )+2 x \left (t \right ) y \left (t \right )]
\]
|
✗ |
✗ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = \sin \left (x \left (t \right )\right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = \sin \left (2 x \left (t \right )\right )-5 y \left (t \right )]
\]
|
✗ |
✗ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = 8 x \left (t \right )-y \left (t \right )^{2}, y^{\prime }\left (t \right ) = 6 x \left (t \right )^{2}-6 y \left (t \right )]
\]
|
✗ |
✗ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )^{2}-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )^{3}-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\]
|
✗ |
✗ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 3 y \left (t \right )^{2}-x \left (t \right )^{2}]
\]
|
✓ |
✓ |
✗ |
|