| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x}\\ y \left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.895 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-y&=2 \,{\mathrm e}^{x}\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.240 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-9 y&=2+x\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.214 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=2+x\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.950 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }+6 y&=-2 \sin \left (3 x \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.224 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+2 y&=-x^{2}+1\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.935 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }&=x +\cos \left (x \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ y^{\prime \prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.340 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-2 y&=6\\ y \left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y&={\mathrm e}^{x}\\ y \left (0\right )&={\frac {5}{2}}\\ \end {array} \]
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.923 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=1\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=18 \,{\mathrm e}^{3 x}\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=6\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.913 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-2 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-2 y&=x^{2}\\ y \left (0\right )&={\frac {11}{4}}\\ y^{\prime }\left (0\right )&={\frac {1}{2}}\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.930 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-2 y^{\prime }+y^{\prime \prime }&=2 \sin \left (x \right )\\ y \left (0\right )&=-2\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
8.140 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=5\\ y^{\prime \prime }\left (0\right )&=5\\ \end {array} \]
Using Laplace transform method. |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le x <1 \\ 1 & 1\le x \end {array}\right .\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
3.655 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-2 y&=\left \{\begin {array}{cc} 1 & 2\le x <4 \\ 0 & \operatorname {otherwise} \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.952 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le x <1 \\ \left (-1+x \right )^{2} & 1\le x \end {array}\right .\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
4.269 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-2 y^{\prime }+y^{\prime \prime }&=\left \{\begin {array}{cc} 0 & 0\le x <1 \\ x^{2}-2 x +3 & 1\le x \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.955 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y+y^{\prime \prime }&=\left \{\begin {array}{cc} 0 & 0\le x <\pi \\ -\sin \left (3 x \right ) & \pi \le x \end {array}\right .\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
18.754 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y&=\left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.185 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+5 y&=\left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right .\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
9.972 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+3 y&=\delta \left (x -2\right )\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.318 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-3 y&=\delta \left (-1+x \right )+2 \operatorname {Heaviside}\left (x -2\right )\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.607 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=\delta \left (x -\pi \right )+\delta \left (x -3 \pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
8.593 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-2 y^{\prime }+y^{\prime \prime }&=2 \delta \left (-1+x \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.398 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+5 y&=\cos \left (x \right )+2 \delta \left (x -\pi \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.064 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y+y^{\prime \prime }&=\cos \left (x \right ) \delta \left (x -\pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.880 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+a^{2} y&=\delta \left (x -\pi \right ) f \left (x \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.313 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}-3 y_{2}\\ y_{2}^{\prime }&=y_{1}-2 y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}-2 y_{2}\\ y_{2}^{\prime }&=y_{1}+3 y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.126 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}+2 y_{2}+x -1\\ y_{2}^{\prime }&=3 y_{1}+2 y_{2}-5 x -2\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.230 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\frac {2 y_{1}}{x}-\frac {y_{2}}{x^{2}}-3+\frac {1}{x}-\frac {1}{x^{2}}\\ y_{2}^{\prime }&=2 y_{1}+1-6 x\\ \end {array} \]
|
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.040 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x\\ y_{2}^{\prime }&=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x\\ \end {array} \]
|
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.038 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=3 y_{1}-2 y_{2}\\ y_{2}^{\prime }&=y_{2}-y_{1}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.231 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right )\\ y_{2}^{\prime }&=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1\\ \end {array} \]
|
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.047 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right )\\ y_{2}^{\prime }&=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1\\ \end {array} \]
|
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.041 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&={\mathrm e}^{-x} y_{1}-\sqrt {x +1}\, y_{2}+x^{2}\\ y_{2}^{\prime }&=\frac {y_{1}}{\left (x -2\right )^{2}}\\ \end {array} \]
|
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.041 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&={\mathrm e}^{-x} y_{1}-\sqrt {x +1}\, y_{2}+x^{2}\\ y_{2}^{\prime }&=\frac {y_{1}}{\left (x -2\right )^{2}}\\ \end {array} \]
|
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.045 |
|
| \(\left [\begin {array}{cc} -2 & -4 \\ 1 & 3 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.514 |
|
| \(\left [\begin {array}{cc} -3 & -1 \\ 2 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.711 |
|
| \(\left [\begin {array}{ccc} 1 & 0 & 1 \\ 0 & 1 & -1 \\ -2 & 0 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.918 |
|
| \(\left [\begin {array}{ccc} 3 & 1 & -1 \\ 1 & 3 & -1 \\ 3 & 3 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.760 |
|
| \(\left [\begin {array}{ccc} 7 & -1 & 6 \\ -10 & 4 & -12 \\ -2 & 1 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
8.032 |
|
| \(\left [\begin {array}{cccc} 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.988 |
|
| \(\left [\begin {array}{cccc} 1 & 3 & 5 & 7 \\ 2 & 6 & 10 & 14 \\ 3 & 9 & 15 & 21 \\ 6 & 18 & 30 & 42 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
1.047 |
|
| \(\left [\begin {array}{ccccc} 1 & 3 & 5 & 2 & 4 \\ 5 & 2 & 4 & 1 & 3 \\ 4 & 1 & 3 & 5 & 2 \\ 3 & 5 & 2 & 4 & 1 \\ 2 & 4 & 1 & 3 & 5 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
29.200 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}-3 y_{2}+5 \,{\mathrm e}^{x}\\ y_{2}^{\prime }&=y_{1}+4 y_{2}-2 \,{\mathrm e}^{-x}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
16.019 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{2}-2 y_{1}+\sin \left (2 x \right )\\ y_{2}^{\prime }&=-3 y_{1}+y_{2}-2 \cos \left (3 x \right )\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
22.823 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{2}\\ y_{2}^{\prime }&=3 y_{1}\\ y_{3}^{\prime }&=2 y_{3}-y_{1}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.663 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 x y_{1}-x^{2} y_{2}+4 x\\ y_{2}^{\prime }&={\mathrm e}^{x} y_{1}+3 \,{\mathrm e}^{-x} y_{2}-\cos \left (3 x \right )\\ \end {array} \]
|
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.037 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}-3 y_{2}\\ y_{2}^{\prime }&=y_{1}-2 y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}-3 y_{2}+4 x -2\\ y_{2}^{\prime }&=y_{1}-2 y_{2}+3 x\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.334 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}\\ y_{2}^{\prime }&=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}\\ \end {array} \]
|
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.040 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x\\ y_{2}^{\prime }&=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x\\ \end {array} \]
|
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.039 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}+y_{2}-2 y_{3}\\ y_{2}^{\prime }&=3 y_{2}-2 y_{3}\\ y_{3}^{\prime }&=3 y_{1}+y_{2}-3 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.310 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=5 y_{1}-5 y_{2}-5 y_{3}\\ y_{2}^{\prime }&=-y_{1}+4 y_{2}+2 y_{3}\\ y_{3}^{\prime }&=3 y_{1}-5 y_{2}-3 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.088 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=4 y_{1}+6 y_{2}+6 y_{3}\\ y_{2}^{\prime }&=y_{1}+3 y_{2}+2 y_{3}\\ y_{3}^{\prime }&=-y_{1}-4 y_{2}-3 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
8.445 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}+2 y_{2}-3 y_{3}\\ y_{2}^{\prime }&=-3 y_{1}+4 y_{2}-2 y_{3}\\ y_{3}^{\prime }&=2 y_{1}+y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.201 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-2 y_{1}-y_{2}+y_{3}\\ y_{2}^{\prime }&=-y_{1}-2 y_{2}-y_{3}\\ y_{3}^{\prime }&=y_{1}-y_{2}-2 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}+y_{2}+2 y_{3}\\ y_{2}^{\prime }&=y_{1}+y_{2}+2 y_{3}\\ y_{3}^{\prime }&=2 y_{1}+2 y_{2}+4 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.138 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}+y_{2}\\ y_{2}^{\prime }&=-y_{1}+2 y_{2}\\ y_{3}^{\prime }&=3 y_{3}-4 y_{4}\\ y_{4}^{\prime }&=4 y_{3}+3 y_{4}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.182 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{2}\\ y_{2}^{\prime }&=-3 y_{1}+2 y_{3}\\ y_{3}^{\prime }&=y_{4}\\ y_{4}^{\prime }&=2 y_{1}-5 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
13.925 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=3 y_{1}+2 y_{2}\\ y_{2}^{\prime }&=3 y_{2}-2 y_{1}\\ y_{3}^{\prime }&=y_{3}\\ y_{4}^{\prime }&=2 y_{4}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.916 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{2}+y_{4}\\ y_{2}^{\prime }&=y_{1}-y_{3}\\ y_{3}^{\prime }&=y_{4}\\ y_{4}^{\prime }&=y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.311 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+3 y\\ y^{\prime }&=2 y-x\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y-x\\ y^{\prime }&=-2 x+3 y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.633 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x-2 y\\ y^{\prime }&=2 x-3 y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
3.798 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x-2 y\\ y^{\prime }&=5 x+y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.897 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y-x\\ y^{\prime }&=-2 x-y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
7.952 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-2 y\\ y^{\prime }&=2 x+y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-5 x-y+2\\ y^{\prime }&=3 x-y-3\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.331 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y-6\\ y^{\prime }&=4 x-y+2\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.694 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {1+y}{1+t} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.704 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=t^{2} y^{2} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
56.678 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=t^{4} y \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.002 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=2 y+1 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.623 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=2-y \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.213 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{-y} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
381.659 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x^{2}+1 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
11.269 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=2 t y^{2}+3 y^{2} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
31.944 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {t}{y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
71.352 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {t}{y+t^{2} y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.235 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=t y^{{1}/{3}} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
102.589 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {1}{2 y+1} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.754 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {2 y+1}{t} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
33.159 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y \left (1-y\right ) \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
15.244 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {4 t}{1+3 y^{2}} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✗ |
456.298 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} v^{\prime }&=t^{2} v-2-2 v+t^{2} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.369 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {1}{t y+t +y+1} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
32.597 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {{\mathrm e}^{t} y}{1+y^{2}} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.978 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y^{2}-4 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
33.786 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} w^{\prime }&=\frac {w}{t} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
38.995 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sec \left (y\right ) \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
13.859 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-t x\\ x \left (0\right )&=\frac {1}{\sqrt {\pi }}\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.105 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=t y\\ y \left (0\right )&=3\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.572 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-y^{2}\\ y \left (0\right )&={\frac {1}{2}}\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
32.866 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=t^{2} y^{3}\\ y \left (0\right )&=-1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
97.421 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-y^{2}\\ y \left (0\right )&=0\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
58.197 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {t}{y-t^{2} y}\\ y \left (0\right )&=4\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
31.134 |
|