| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.431 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.550 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.279 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.260 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.696 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.210 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +10 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
4.713 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.102 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 y^{\prime } x -8 y&=0 \\
\end{align*} |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
✓ |
✓ |
✓ |
0.100 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-6 y^{\prime } x +18 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.101 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=4 x -6 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.059 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=2 x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.033 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=4 \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
5.060 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=2 x \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.816 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=4 \sin \left (\ln \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.092 |
|
| \begin{align*}
-2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x^{3} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.240 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x -10 y&=0 \\
y \left (1\right ) &= 5 \\
y^{\prime }\left (1\right ) &= 4 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.705 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y \left (2\right ) &= 0 \\
y^{\prime }\left (2\right ) &= 4 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.407 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +3 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -5 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.223 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y&=4 x -8 \\
y \left (1\right ) &= 4 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.481 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=-6 x^{3}+4 x^{2} \\
y \left (2\right ) &= 4 \\
y^{\prime }\left (2\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.622 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=10 x^{2} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -6 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.410 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=2 x^{3} \\
y \left (2\right ) &= 0 \\
y^{\prime }\left (2\right ) &= -8 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.850 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-6 y&=\ln \left (x \right ) \\
y \left (1\right ) &= {\frac {1}{6}} \\
y^{\prime }\left (1\right ) &= -{\frac {1}{6}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.309 |
|
| \begin{align*}
\left (2+x \right )^{2} y^{\prime \prime }-\left (2+x \right ) y^{\prime }-3 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
21.763 |
|
| \begin{align*}
\left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
45.301 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.292 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime } x -4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.290 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.287 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x +\left (x^{2}-4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.290 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x +\left (3 x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.340 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x +\left (3 x -2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.357 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-\left (3 x -2\right ) y^{\prime }+2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \begin{align*}
\left (x^{3}-1\right ) y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.339 |
|
| \begin{align*}
\left (x +3\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.373 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x -y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.262 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x -2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.259 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +2 y x&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \begin{align*}
\left (2 x^{2}-3\right ) y^{\prime \prime }-2 y^{\prime } x +y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=1\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.389 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=1\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.440 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }+2 y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 4 \\
\end{align*} Series expansion around \(x=1\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.459 |
|
| \begin{align*}
\left (x^{2}-3 x \right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| \begin{align*}
\left (x^{3}+x^{2}\right ) y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.046 |
|
| \begin{align*}
\left (x^{4}-2 x^{3}+x^{2}\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.141 |
|
| \begin{align*}
\left (x^{5}+x^{4}-6 x^{3}\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.102 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}-3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.461 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+\frac {8}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +\left (2 x^{2}+\frac {5}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.484 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| \begin{align*}
2 y^{\prime \prime } x +y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| \begin{align*}
3 y^{\prime \prime } x -\left (x -2\right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.607 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{4}+x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \begin{align*}
y^{\prime \prime } x -\left (x^{2}+2\right ) y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.571 |
|
| \begin{align*}
\left (2 x^{2}-x \right ) y^{\prime \prime }+\left (2 x -2\right ) y^{\prime }+\left (-2 x^{2}+3 x -2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +\frac {3 y}{4}&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.539 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.559 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +8 \left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.525 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\frac {3 y}{4}&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \begin{align*}
2 y^{\prime \prime } x +6 y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.308 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}-3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.504 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-2 x-4 y&={\mathrm e}^{t} \\
x^{\prime }+y^{\prime }-y&={\mathrm e}^{4 t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.208 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-x&=-2 t \\
x^{\prime }+y^{\prime }-3 x-y&=t^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.178 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-x-3 y&={\mathrm e}^{t} \\
x^{\prime }+y^{\prime }+x&={\mathrm e}^{3 t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.138 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-x-2 y&=2 \,{\mathrm e}^{t} \\
x^{\prime }+y^{\prime }-3 x-4 y&={\mathrm e}^{2 t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.083 |
|
| \begin{align*}
2 x^{\prime }+y^{\prime }-x-y&={\mathrm e}^{-t} \\
x^{\prime }+2 x+y^{\prime }+y&={\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| \begin{align*}
2 x^{\prime }+y^{\prime }-3 x-y&=t \\
x^{\prime }+y^{\prime }-4 x-y&={\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-x-6 y&={\mathrm e}^{3 t} \\
x^{\prime }+2 y^{\prime }-2 x-6 y&=t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-x-3 y&=3 t \\
x^{\prime }+2 y^{\prime }-2 x-3 y&=1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| \begin{align*}
x^{\prime }+y^{\prime }+2 y&=\sin \left (t \right ) \\
x^{\prime }+y^{\prime }-x-y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.201 |
|
| \begin{align*}
x^{\prime }-y^{\prime }-2 x+4 y&=t \\
x^{\prime }+y^{\prime }-x-y&=1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.024 |
|
| \begin{align*}
2 x^{\prime }+y^{\prime }+x+5 y&=4 t \\
x^{\prime }+y^{\prime }+2 x+2 y&=2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-x+5 y&=t^{2} \\
x^{\prime }+2 y^{\prime }-2 x+4 y&=2 t +1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.605 |
|
| \begin{align*}
2 x^{\prime }+y^{\prime }+x+y&=t^{2}+4 t \\
x^{\prime }+y^{\prime }+2 x+2 y&=2 t^{2}-2 t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| \begin{align*}
3 x^{\prime }+2 y^{\prime }-x+y&=t -1 \\
x^{\prime }+y^{\prime }-x&=t +2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| \begin{align*}
2 x^{\prime }+4 y^{\prime }+x-y&=3 \,{\mathrm e}^{t} \\
x^{\prime }+y^{\prime }+2 x+2 y&={\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| \begin{align*}
2 x^{\prime }+y^{\prime }-x-y&=-2 t \\
x^{\prime }+y^{\prime }+x-y&=t^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| \begin{align*}
2 x^{\prime }+y^{\prime }-x-y&=1 \\
x^{\prime }+y^{\prime }+2 x-y&=t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \begin{align*}
x^{\prime }&=3 x+4 y \\
y^{\prime }&=2 x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| \begin{align*}
x^{\prime }&=5 x+3 y \\
y^{\prime }&=4 x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 8 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
x^{\prime }&=5 x+2 y+5 t \\
y^{\prime }&=3 x+4 y+17 t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.574 |
|
| \begin{align*}
x^{\prime }&=5 x-2 y \\
y^{\prime }&=4 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| \begin{align*}
x^{\prime }&=5 x-y \\
y^{\prime }&=3 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.340 |
|
| \begin{align*}
x^{\prime }&=-2 x+7 y \\
y^{\prime }&=3 x+2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 9 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=7 x+4 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 6 \\
y \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.370 |
|
| \(\left [\begin {array}{cc} 1 & 2 \\ 3 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.204 |
|
| \(\left [\begin {array}{cc} 3 & 2 \\ 6 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.214 |
|
| \(\left [\begin {array}{cc} 3 & 1 \\ 12 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.216 |
|
| \(\left [\begin {array}{cc} -2 & 7 \\ 3 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.209 |
|
| \(\left [\begin {array}{cc} 3 & 4 \\ 5 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.216 |
|
| \(\left [\begin {array}{cc} 3 & -5 \\ -4 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.211 |
|