| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \(\left [\begin {array}{ccc} 1 & 1 & -1 \\ 2 & 3 & -4 \\ 4 & 1 & -4 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.669 |
|
| \(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & -6 & 6 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.728 |
|
| \(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & 1 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.686 |
|
| \(\left [\begin {array}{ccc} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
3.972 |
|
| \(\left [\begin {array}{ccc} 1 & 3 & -6 \\ 0 & 2 & 2 \\ 0 & -1 & 5 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.675 |
|
| \(\left [\begin {array}{ccc} -5 & -12 & 6 \\ 1 & 5 & -1 \\ -7 & -10 & 8 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.748 |
|
| \(\left [\begin {array}{ccc} -2 & 5 & 5 \\ -1 & 4 & 5 \\ 3 & -3 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.672 |
|
| \(\left [\begin {array}{ccc} -2 & 6 & -18 \\ 12 & -23 & 66 \\ 5 & -10 & 29 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.735 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y-z\\ y^{\prime }&=2 x+3 y-4 z\\ z^{\prime }&=4 x+y-4 z\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.070 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y-z\\ y^{\prime }&=x+3 y+z\\ z^{\prime }&=-3 x-6 y+6 z\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
4.688 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime }&={\mathrm e}^{3 t}\\ y \left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.626 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y^{\prime }&=2 \sin \left (t \right )\\ y \left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }+6 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.211 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-12 y&=0\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.298 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=8\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=6\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.382 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+5 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=4\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-2 y&=18 \,{\mathrm e}^{-t} \sin \left (3 t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=t \,{\mathrm e}^{-2 t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.403 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+7 y^{\prime }+10 y&=4 t \,{\mathrm e}^{-3 t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.399 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-8 y^{\prime }+15 y&=9 \,{\mathrm e}^{2 t} t\\ y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=10\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y&=20 \sin \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=-2\\ \end {array} \]
Using Laplace transform method. |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=36 t \,{\mathrm e}^{4 t}\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=-6\\ \end {array} \]
Using Laplace transform method. |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 2 & 0<t <4 \\ 0 & 4<t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.210 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }+6 y&=\left \{\begin {array}{cc} 6 & 0<t <2 \\ 0 & 2<t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.679 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+5 y&=\left \{\begin {array}{cc} 1 & 0<t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.556 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+6 y^{\prime }+8 y&=\left \{\begin {array}{cc} 3 & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right .\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.007 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} -4 t +8 \pi & 0<t <2 \pi \\ 0 & 2<t \end {array}\right .\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0<t <\pi \\ \pi & \pi <t \end {array}\right .\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.745 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime \prime }-2 x^{\prime }+9 t^{5} x&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.895 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{3} x^{\prime \prime \prime }-3 t^{2} x^{\prime \prime }+6 t x^{\prime }-6 x&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.216 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t^{3}-2 t^{2}\right ) x^{\prime \prime }-\left (t^{3}+2 t^{2}-6 t \right ) x^{\prime }+\left (3 t^{2}-6\right ) x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.002 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{3} x^{\prime \prime \prime }-\left (t +3\right ) t^{2} x^{\prime \prime }+2 t \left (t +3\right ) x^{\prime }-2 \left (t +3\right ) x&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.115 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} x^{\prime \prime }+3 t x^{\prime }+3 x&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
5.839 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 t +1\right ) x^{\prime \prime }+t^{3} x^{\prime }+x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
54.053 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} x^{\prime \prime }+\left (2 t^{3}+7 t \right ) x^{\prime }+\left (8 t^{2}+8\right ) x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.235 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{3} x^{\prime \prime }-\left (t^{3}+2 t^{2}-t \right ) x^{\prime }+\left (t^{2}+t -1\right ) x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.199 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{3} x^{\prime \prime }+3 t^{2} x^{\prime }+x&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.374 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (t \right ) x^{\prime \prime }+\cos \left (t \right ) x^{\prime }+2 x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
7.344 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {\left (1+t \right ) x^{\prime \prime }}{t}-\frac {x^{\prime }}{t^{2}}+\frac {x}{t^{3}}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.340 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} x^{\prime \prime }+t x^{\prime }+x&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.332 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t^{4}+t^{2}\right ) x^{\prime \prime }+2 t^{3} x^{\prime }+3 x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
82.876 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-\tan \left (t \right ) x^{\prime }+x&=0 \end {array} \]
|
[_Lienard] |
✗ |
✓ |
✓ |
✗ |
9.522 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} f \left (t \right ) x^{\prime \prime }+x g \left (t \right )&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
3.154 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+\left (1+t \right ) x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.149 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\lambda y&=0\\ y \left (0\right )&=0\\ y \left (\frac {\pi }{2}\right )&=0\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.620 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\lambda y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (\pi \right )&=0\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.653 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\lambda y&=0\\ y \left (0\right )&=0\\ y \left (L \right )&=0\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.674 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\lambda y&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime }\left (L \right )&=0\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
47.841 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +y^{\prime }+\frac {\lambda y}{x}&=0\\ y \left (1\right )&=0\\ y \left ({\mathrm e}^{\pi }\right )&=0\\ \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.279 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +y^{\prime }+\frac {\lambda y}{x}&=0\\ y \left (1\right )&=0\\ y^{\prime }\left ({\mathrm e}^{\pi }\right )&=0\\ \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.981 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }+\frac {\lambda y}{x^{2}+1}&=0\\ y \left (0\right )&=0\\ y \left (1\right )&=0\\ \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
6.050 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\frac {6 y^{\prime } x}{\left (3 x^{2}+1\right )^{2}}+\frac {y^{\prime \prime }}{3 x^{2}+1}+\lambda \left (3 x^{2}+1\right ) y&=0\\ y \left (0\right )&=0\\ y \left (\pi \right )&=0\\ \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.180 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+3 y\\ y^{\prime }&=3 x+y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.508 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+2 y\\ y^{\prime }&=x+2 y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.577 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+4 y\\ y^{\prime }&=3 x+2 y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.545 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+5 y\\ y^{\prime }&=x-2 y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-4 y\\ y^{\prime }&=2 x-2 y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-2 y\\ y^{\prime }&=4 x+5 y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.811 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y\\ y^{\prime }&=x+5 y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
4.261 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+7 y\\ y^{\prime }&=3 x+5 y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.650 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=3 x-y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=a x+b y\\ y^{\prime }&=c x+d y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.485 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-4 y-x \left (x^{2}+y^{2}\right )\\ y^{\prime }&=4 x+4 y-y \left (x^{2}+y^{2}\right )\\ \end {array} \]
|
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.031 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y+\frac {x \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}}\\ y^{\prime }&=-x+\frac {y \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}}\\ \end {array} \]
|
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.105 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+x^{4} x^{\prime }-x^{\prime }+x&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
158.386 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+x^{\prime }+{x^{\prime }}^{3}+x&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
62.868 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+\left (x^{4}+x^{2}\right ) x^{\prime }+x^{3}+x&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
210.177 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3}&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
56.100 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+\left (x^{2}+1\right ) x^{\prime }+x^{3}&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
36.279 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-x^{2}\\ y^{\prime }&=2 y-y^{2}\\ \end {array} \]
|
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.032 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\sin \left (t \right )+\cos \left (t \right ) \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {1}{x^{2}-1} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.972 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime }&=4 t \ln \left (t \right ) \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.751 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{\prime }&={\mathrm e}^{-2 x} x \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.660 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} T^{\prime }&={\mathrm e}^{-t} \sin \left (2 t \right ) \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.144 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\sec \left (t \right )^{2}\\ x \left (\frac {\pi }{4}\right )&=0\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.736 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x -\frac {1}{3} x^{3}\\ y \left (-1\right )&=1\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 \sin \left (t \right )^{2}\\ x \left (\frac {\pi }{4}\right )&=\frac {\pi }{4}\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.837 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x V^{\prime }&=x^{2}+1\\ V \left (1\right )&=1\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.897 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t}&={\mathrm e}^{-t}\\ x \left (0\right )&=3\\ \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
93.054 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=1-x \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.499 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x \left (2-x\right ) \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.693 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\left (1+x\right ) \left (2-x\right ) \sin \left (x\right ) \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
16.030 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x \left (1-x\right ) \left (2-x\right ) \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
11.964 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x^{2}-x^{4} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.823 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=t^{3} \left (1-x\right )\\ x \left (0\right )&=3\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.753 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\left (1+y^{2}\right ) \tan \left (x \right )\\ y \left (0\right )&=1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✗ |
✓ |
19.162 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=t^{2} x \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.127 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x^{2} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.012 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y^{2} {\mathrm e}^{-t^{2}} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.772 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+p x&=q \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.742 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x&=k y \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.670 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} i^{\prime }&=p \left (t \right ) i \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.085 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\lambda x \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.184 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} m v^{\prime }&=-m g +k v^{2} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.186 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=k x-x^{2}\\ x \left (0\right )&=x_{0}\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
347.341 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x \left (k^{2}+x^{2}\right )\\ x \left (0\right )&=x_{0}\\ \end {array} \]
|
[_quadrature] |
✓ |
✗ |
✓ |
✗ |
381.379 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\frac {y}{x}&=x^{2} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.235 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+t x&=4 t\\ x \left (0\right )&=2\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.053 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{\prime }&=z \tan \left (y \right )+\sin \left (y \right ) \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.876 |
|