| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }-4 y&=x \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=72 x^{5} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.708 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.632 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{4} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.165 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-4 y^{\prime } x +3 y&=8 x^{{4}/{3}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.427 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.500 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{2}-1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.889 |
|
| \begin{align*}
x^{\prime \prime }+9 x&=10 \cos \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=5 \sin \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \begin{align*}
x^{\prime \prime }+100 x&=225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \\
x \left (0\right ) &= 375 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| \begin{align*}
x^{\prime \prime }+25 x&=90 \cos \left (4 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 90 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \begin{align*}
m x^{\prime \prime }+k x&=F_{0} \cos \left (\omega t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+4 x&=10 \cos \left (3 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.503 |
|
| \begin{align*}
x^{\prime \prime }+3 x^{\prime }+5 x&=-4 \cos \left (5 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| \begin{align*}
2 x^{\prime \prime }+2 x^{\prime }+x&=3 \sin \left (10 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| \begin{align*}
x^{\prime \prime }+3 x^{\prime }+3 x&=8 \cos \left (10 t \right )+6 \sin \left (10 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.514 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+5 x&=10 \cos \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} | [[_2nd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✓ | 0.678 |
|
| \begin{align*}
x^{\prime \prime }+6 x^{\prime }+13 x&=10 \sin \left (5 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.604 |
|
| \begin{align*}
x^{\prime \prime }+6 x^{\prime }+13 x&=10 \sin \left (5 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+26 x&=600 \cos \left (10 t \right ) \\
x \left (0\right ) &= 10 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| \begin{align*}
x^{\prime \prime }+8 x^{\prime }+25 x&=200 \cos \left (t \right )+520 \sin \left (t \right ) \\
x \left (0\right ) &= -30 \\
x^{\prime }\left (0\right ) &= -10 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.601 |
|
| \begin{align*}
x^{\prime }&=-3 y \\
y^{\prime }&=3 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| \begin{align*}
x^{\prime }&=2 x+4 y+3 \,{\mathrm e}^{t} \\
y^{\prime }&=5 x-y-t^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.740 |
|
| \begin{align*}
x^{\prime }&=y+z \\
y^{\prime }&=x+z \\
z^{\prime }&=x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=2 x_{3} \\
x_{3}^{\prime }&=3 x_{4} \\
x_{4}^{\prime }&=4 x_{1} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.036 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2}+x_{3}+1 \\
x_{2}^{\prime }&=x_{3}+x_{4}+t \\
x_{3}^{\prime }&=x_{1}+x_{4}+t^{2} \\
x_{4}^{\prime }&=x_{1}+x_{2}+t^{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.355 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.089 |
|
| \begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.096 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.098 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime \prime }-\left (2+x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.089 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.084 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.105 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.158 |
|
| \begin{align*}
5 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.064 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+16 y^{\prime \prime }&=0 \\
\end{align*} | [[_high_order, _missing_x]] | ✓ | ✓ | ✓ | ✓ | 0.076 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.044 |
|
| \begin{align*}
9 y^{\prime \prime \prime }+12 y^{\prime \prime }+4 y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.040 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.066 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-16 y^{\prime \prime }+16 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.086 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.050 |
|
| \begin{align*}
6 y^{\prime \prime \prime \prime }+11 y^{\prime \prime }+4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }&=16 y \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.040 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.039 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.062 |
|
| \begin{align*}
2 y^{\prime \prime \prime }-3 y^{\prime \prime }-2 y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
y^{\prime \prime }\left (0\right ) &= 3 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.072 |
|
| \begin{align*}
3 y^{\prime \prime \prime }+2 y^{\prime \prime }&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.076 |
|
| \begin{align*}
y^{\prime \prime \prime }+10 y^{\prime \prime }+25 y^{\prime }&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 4 \\
y^{\prime \prime }\left (0\right ) &= 5 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.083 |
|
| \begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.044 |
|
| \begin{align*}
2 y^{\prime \prime \prime }-y^{\prime \prime }-5 y^{\prime }-2 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| \begin{align*}
y^{\prime \prime \prime }+27 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-6 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.059 |
|
| \begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }-8 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.051 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.057 |
|
| \begin{align*}
y^{\prime \prime \prime }-5 y^{\prime \prime }+100 y^{\prime }-500 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 10 \\
y^{\prime \prime }\left (0\right ) &= 250 \\
\end{align*} | [[_3rd_order, _missing_x]] | ✓ | ✓ | ✓ | ✓ | 0.108 |
|
| \begin{align*}
y^{\prime \prime \prime }&=y \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.095 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }&=y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+2 y \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 15 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.123 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 y^{\prime } x&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.119 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+y^{\prime } x&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.112 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+y^{\prime } x&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.114 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+y^{\prime } x&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.118 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 y^{\prime } x +y&=0 \\
\end{align*} |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.112 |
|
| \begin{align*}
x_{1}^{\prime }&=6 x_{1} \\
x_{2}^{\prime }&=-3 x_{1}-x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.356 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-3 x_{1}+4 x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.397 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+3 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.382 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+4 x_{2} \\
x_{2}^{\prime }&=3 x_{1}+2 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2} \\
x_{2}^{\prime }&=6 x_{1}-x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.385 |
|
| \begin{align*}
x_{1}^{\prime }&=6 x_{1}-7 x_{2} \\
x_{2}^{\prime }&=x_{1}-2 x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
x_{1}^{\prime }&=9 x_{1}+5 x_{2} \\
x_{2}^{\prime }&=-6 x_{1}-2 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\
x_{2}^{\prime }&=6 x_{1}-5 x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\
x_{2}^{\prime }&=4 x_{1}-2 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=9 x_{1}+3 x_{2} \\
\end{align*} | system_of_ODEs | ✓ | ✓ | ✓ | ✓ | 0.430 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 4 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.443 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}+3 x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.528 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}-9 x_{2} \\
x_{2}^{\prime }&=2 x_{1}-x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\
x_{2}^{\prime }&=4 x_{1}+3 x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.391 |
|
| \begin{align*}
x_{1}^{\prime }&=7 x_{1}-5 x_{2} \\
x_{2}^{\prime }&=4 x_{1}+3 x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| \begin{align*}
x_{1}^{\prime }&=-50 x_{1}+20 x_{2} \\
x_{2}^{\prime }&=100 x_{1}-60 x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\
x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3} \\
x_{3}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.650 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=2 x_{1}+7 x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}+7 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+4 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2}+4 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}+x_{2}+3 x_{3} \\
x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3} \\
x_{3}^{\prime }&=3 x_{1}+x_{2}+5 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}-6 x_{3} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}-2 x_{3} \\
x_{3}^{\prime }&=4 x_{1}-2 x_{2}-4 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+2 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=-5 x_{1}-4 x_{2}-2 x_{3} \\
x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=-5 x_{1}-3 x_{2}-x_{3} \\
x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.645 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
x_{2}^{\prime }&=-4 x_{1}-3 x_{2}-x_{3} \\
x_{3}^{\prime }&=4 x_{1}+4 x_{2}+2 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}+5 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=-6 x_{1}-6 x_{2}-5 x_{3} \\
x_{3}^{\prime }&=6 x_{1}+6 x_{2}+5 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.895 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+x_{3} \\
x_{2}^{\prime }&=9 x_{1}-x_{2}+2 x_{3} \\
x_{3}^{\prime }&=-9 x_{1}+4 x_{2}-x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
x_{3} \left (0\right ) &= 17 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.971 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=2 x_{1}+2 x_{2} \\
x_{3}^{\prime }&=3 x_{2}+3 x_{3} \\
x_{4}^{\prime }&=4 x_{3}+4 x_{4} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.047 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}+9 x_{4} \\
x_{2}^{\prime }&=4 x_{1}+2 x_{2}-10 x_{4} \\
x_{3}^{\prime }&=-x_{3}+8 x_{4} \\
x_{4}^{\prime }&=x_{4} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1} \\
x_{2}^{\prime }&=-21 x_{1}-5 x_{2}-27 x_{3}-9 x_{4} \\
x_{3}^{\prime }&=5 x_{3} \\
x_{4}^{\prime }&=-21 x_{3}-2 x_{4} \\
\end{align*} | system_of_ODEs | ✓ | ✓ | ✓ | ✓ | 1.157 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3}+7 x_{4} \\
x_{2}^{\prime }&=x_{1}+4 x_{2}+10 x_{3}+x_{4} \\
x_{3}^{\prime }&=x_{1}+10 x_{2}+4 x_{3}+x_{4} \\
x_{4}^{\prime }&=7 x_{1}+x_{2}+x_{3}+4 x_{4} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 3 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
x_{4} \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.158 |
|
| \begin{align*}
x_{1}^{\prime }&=-40 x_{1}-12 x_{2}+54 x_{3} \\
x_{2}^{\prime }&=35 x_{1}+13 x_{2}-46 x_{3} \\
x_{3}^{\prime }&=-25 x_{1}-7 x_{2}+34 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| \begin{align*}
x_{1}^{\prime }&=-20 x_{1}+11 x_{2}+13 x_{3} \\
x_{2}^{\prime }&=12 x_{1}-x_{2}-7 x_{3} \\
x_{3}^{\prime }&=-48 x_{1}+21 x_{2}+31 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.755 |
|
| \begin{align*}
x_{1}^{\prime }&=147 x_{1}+23 x_{2}-202 x_{3} \\
x_{2}^{\prime }&=-90 x_{1}-9 x_{2}+129 x_{3} \\
x_{3}^{\prime }&=90 x_{1}+15 x_{2}-123 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| \begin{align*}
x_{1}^{\prime }&=9 x_{1}-7 x_{2}-5 x_{3} \\
x_{2}^{\prime }&=-12 x_{1}+7 x_{2}+11 x_{3}+9 x_{4} \\
x_{3}^{\prime }&=24 x_{1}-17 x_{2}-19 x_{3}-9 x_{4} \\
x_{4}^{\prime }&=-18 x_{1}+13 x_{2}+17 x_{3}+9 x_{4} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.022 |
|
| \begin{align*}
x_{1}^{\prime }&=13 x_{1}-42 x_{2}+106 x_{3}+139 x_{4} \\
x_{2}^{\prime }&=2 x_{1}-16 x_{2}+52 x_{3}+70 x_{4} \\
x_{3}^{\prime }&=x_{1}+6 x_{2}-20 x_{3}-31 x_{4} \\
x_{4}^{\prime }&=-x_{1}-6 x_{2}+22 x_{3}+33 x_{4} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.520 |
|
| \begin{align*}
x_{1}^{\prime }&=23 x_{1}-18 x_{2}-16 x_{3} \\
x_{2}^{\prime }&=-8 x_{1}+6 x_{2}+7 x_{3}+9 x_{4} \\
x_{3}^{\prime }&=34 x_{1}-27 x_{2}-26 x_{3}-9 x_{4} \\
x_{4}^{\prime }&=-26 x_{1}+21 x_{2}+25 x_{3}+12 x_{4} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.284 |
|