| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&={\mathrm e}^{x} \\
y \left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.083 |
|
| \begin{align*}
y^{\prime }-y&=2 \,{\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.097 |
|
| \begin{align*}
y^{\prime \prime }-9 y&=2+x \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.121 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=2+x \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.139 |
|
| \begin{align*}
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{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.217 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=-x^{2}+1 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.131 |
|
| \begin{align*}
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{align*} Using Laplace transform method. |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.210 |
|
| \begin{align*}
y^{\prime }-2 y&=6 \\
y \left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.099 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{x} \\
y \left (0\right ) &= {\frac {5}{2}} \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.112 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.111 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=18 \,{\mathrm e}^{3 x} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.132 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.093 |
|
| \begin{align*}
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{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.129 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 \sin \left (x \right ) \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.134 |
|
| \begin{align*}
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{align*} Using Laplace transform method. |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.178 |
|
| \begin{align*}
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{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
0.320 |
|
| \begin{align*}
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{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.449 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le x <1 \\ \left (x -1\right )^{2} & 1\le x \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.392 |
|
| \begin{align*}
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{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.516 |
|
| \begin{align*}
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{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.865 |
|
| \begin{align*}
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{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.485 |
|
| \begin{align*}
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{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.211 |
|
| \begin{align*}
y^{\prime }+3 y&=\delta \left (x -2\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.276 |
|
| \begin{align*}
y^{\prime }-3 y&=\delta \left (x -1\right )+2 \operatorname {Heaviside}\left (x -2\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
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{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 \delta \left (x -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.400 |
|
| \begin{align*}
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{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.709 |
|
| \begin{align*}
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{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.230 |
|
| \begin{align*}
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{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.321 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}-3 y_{2} \\
y_{2}^{\prime }&=y_{1}-2 y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}-2 y_{2} \\
y_{2}^{\prime }&=y_{1}+3 y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.455 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}+2 y_{2}+x -1 \\
y_{2}^{\prime }&=3 y_{1}+2 y_{2}-5 x -2 \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -2 \\
y_{2} \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
y_{1} \left (1\right ) &= -2 \\
y_{2} \left (1\right ) &= -5 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.037 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
y_{1} \left (-1\right ) &= 3 \\
y_{2} \left (-1\right ) &= -3 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.043 |
|
| \begin{align*}
y_{1}^{\prime }&=3 y_{1}-2 y_{2} \\
y_{2}^{\prime }&=y_{2}-y_{1} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
y_{1} \left (1\right ) &= 1 \\
y_{2} \left (1\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.043 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
y_{1} \left (2\right ) &= 1 \\
y_{2} \left (2\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.043 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.041 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
y_{1} \left (3\right ) &= 1 \\
y_{2} \left (3\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.041 |
|
| \(\left [\begin {array}{cc} -2 & -4 \\ 1 & 3 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.205 |
|
| \(\left [\begin {array}{cc} -3 & -1 \\ 2 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.257 |
|
| \(\left [\begin {array}{ccc} 1 & 0 & 1 \\ 0 & 1 & -1 \\ -2 & 0 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.813 |
|
| \(\left [\begin {array}{ccc} 3 & 1 & -1 \\ 1 & 3 & -1 \\ 3 & 3 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.341 |
|
| \(\left [\begin {array}{ccc} 7 & -1 & 6 \\ -10 & 4 & -12 \\ -2 & 1 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.768 |
|
| \(\left [\begin {array}{cccc} 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.815 |
|
| \(\left [\begin {array}{cccc} 1 & 3 & 5 & 7 \\ 2 & 6 & 10 & 14 \\ 3 & 9 & 15 & 21 \\ 6 & 18 & 30 & 42 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.849 |
|
| \(\left [\begin {array}{ccccc} 1 & 3 & 5 & 2 & 4 \\ 5 & 2 & 4 & 1 & 3 \\ 4 & 1 & 3 & 5 & 2 \\ 3 & 5 & 2 & 4 & 1 \\ 2 & 4 & 1 & 3 & 5 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
7.920 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.977 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
4.007 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{2} \\
y_{2}^{\prime }&=3 y_{1} \\
y_{3}^{\prime }&=2 y_{3}-y_{1} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.111 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.039 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}-3 y_{2} \\
y_{2}^{\prime }&=y_{1}-2 y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}-3 y_{2}+4 x -2 \\
y_{2}^{\prime }&=y_{1}-2 y_{2}+3 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.034 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.035 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.943 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.374 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.055 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.454 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.840 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.879 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.863 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
5.064 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.388 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.099 |
|
| \begin{align*}
x^{\prime }&=-2 x+3 y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=-2 x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.290 |
|
| \begin{align*}
x^{\prime }&=-x-2 y \\
y^{\prime }&=2 x-3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| \begin{align*}
x^{\prime }&=-x-2 y \\
y^{\prime }&=5 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.415 |
|
| \begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=-2 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.371 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.371 |
|
| \begin{align*}
x^{\prime }&=-5 x-y+2 \\
y^{\prime }&=3 x-y-3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y-6 \\
y^{\prime }&=4 x-y+2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.365 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y}{1+t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.795 |
|
| \begin{align*}
y^{\prime }&=t^{2} y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.977 |
|
| \begin{align*}
y^{\prime }&=t^{4} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.254 |
|
| \begin{align*}
y^{\prime }&=2 y+1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.380 |
|
| \begin{align*}
y^{\prime }&=2-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
x^{\prime }&=x^{2}+1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.050 |
|
| \begin{align*}
y^{\prime }&=2 t y^{2}+3 y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.348 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.869 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{y+t^{2} y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.076 |
|
| \begin{align*}
y^{\prime }&=t y^{{1}/{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.697 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{2 y+1} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.565 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y+1}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.361 |
|
| \begin{align*}
y^{\prime }&=y \left (1-y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.077 |
|
| \begin{align*}
y^{\prime }&=\frac {4 t}{1+3 y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
2.078 |
|
| \begin{align*}
v^{\prime }&=t^{2} v-2-2 v+t^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.041 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{t y+t +y+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.735 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{t} y}{1+y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.756 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.174 |
|
| \begin{align*}
w^{\prime }&=\frac {w}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.746 |
|
| \begin{align*}
y^{\prime }&=\sec \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.968 |
|
| \begin{align*}
x^{\prime }&=-t x \\
x \left (0\right ) &= \frac {1}{\sqrt {\pi }} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.153 |
|
| \begin{align*}
y^{\prime }&=t y \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.235 |
|
| \begin{align*}
y^{\prime }&=-y^{2} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.878 |
|
| \begin{align*}
y^{\prime }&=t^{2} y^{3} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.950 |
|
| \begin{align*}
y^{\prime }&=-y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.325 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{y-t^{2} y} \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.545 |
|