|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-3 y_{2}+4 x -2 \\ y_{2}^{\prime }=y_{1}-2 y_{2}+3 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.456 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x} \\ y_{2}^{\prime }=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.035 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x \\ y_{2}^{\prime }=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.035 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}+y_{2}-2 y_{3} \\ y_{2}^{\prime }=3 y_{2}-2 y_{3} \\ y_{3}^{\prime }=3 y_{1}+y_{2}-3 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.436 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=5 y_{1}-5 y_{2}-5 y_{3} \\ y_{2}^{\prime }=-y_{1}+4 y_{2}+2 y_{3} \\ y_{3}^{\prime }=3 y_{1}-5 y_{2}-3 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.689 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}+6 y_{2}+6 y_{3} \\ y_{2}^{\prime }=y_{1}+3 y_{2}+2 y_{3} \\ y_{3}^{\prime }=-y_{1}-4 y_{2}-3 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.490 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+2 y_{2}-3 y_{3} \\ y_{2}^{\prime }=-3 y_{1}+4 y_{2}-2 y_{3} \\ y_{3}^{\prime }=2 y_{1}+y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.766 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-2 y_{1}-y_{2}+y_{3} \\ y_{2}^{\prime }=-y_{1}-2 y_{2}-y_{3} \\ y_{3}^{\prime }=y_{1}-y_{2}-2 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.398 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+y_{2}+2 y_{3} \\ y_{2}^{\prime }=y_{1}+y_{2}+2 y_{3} \\ y_{3}^{\prime }=2 y_{1}+2 y_{2}+4 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.372 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}+y_{2} \\ y_{2}^{\prime }=-y_{1}+2 y_{2} \\ y_{3}^{\prime }=3 y_{3}-4 y_{4} \\ y_{4}^{\prime }=4 y_{3}+3 y_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.835 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2} \\ y_{2}^{\prime }=-3 y_{1}+2 y_{3} \\ y_{3}^{\prime }=y_{4} \\ y_{4}^{\prime }=2 y_{1}-5 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
4.731 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+2 y_{2} \\ y_{2}^{\prime }=3 y_{2}-2 y_{1} \\ y_{3}^{\prime }=y_{3} \\ y_{4}^{\prime }=2 y_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.698 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2}+y_{4} \\ y_{2}^{\prime }=y_{1}-y_{3} \\ y_{3}^{\prime }=y_{4} \\ y_{4}^{\prime }=y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.468 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+3 y \\ y^{\prime }=-x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.438 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=-2 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.410 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.704 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=5 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.553 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.503 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.503 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x-y+2 \\ y^{\prime }=3 x-y-3 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.618 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y-6 \\ y^{\prime }=4 x-y+2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.979 |
|
|
\[
{}y^{\prime } = \frac {y+1}{t +1}
\] |
[_separable] |
✓ |
1.990 |
|
|
\[
{}y^{\prime } = t^{2} y^{2}
\] |
[_separable] |
✓ |
2.217 |
|
|
\[
{}y^{\prime } = t^{4} y
\] |
[_separable] |
✓ |
1.648 |
|
|
\[
{}y^{\prime } = 2 y+1
\] |
[_quadrature] |
✓ |
1.486 |
|
|
\[
{}y^{\prime } = 2-y
\] |
[_quadrature] |
✓ |
1.405 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-y}
\] |
[_quadrature] |
✓ |
1.602 |
|
|
\[
{}x^{\prime } = 1+x^{2}
\] |
[_quadrature] |
✓ |
3.373 |
|
|
\[
{}y^{\prime } = 2 t y^{2}+3 y^{2}
\] |
[_separable] |
✓ |
2.001 |
|
|
\[
{}y^{\prime } = \frac {t}{y}
\] |
[_separable] |
✓ |
4.408 |
|
|
\[
{}y^{\prime } = \frac {t}{t^{2} y+y}
\] |
[_separable] |
✓ |
1.942 |
|
|
\[
{}y^{\prime } = t y^{{1}/{3}}
\] |
[_separable] |
✓ |
6.908 |
|
|
\[
{}y^{\prime } = \frac {1}{2 y+1}
\] |
[_quadrature] |
✓ |
1.877 |
|
|
\[
{}y^{\prime } = \frac {2 y+1}{t}
\] |
[_separable] |
✓ |
2.260 |
|
|
\[
{}y^{\prime } = y \left (1-y\right )
\] |
[_quadrature] |
✓ |
2.281 |
|
|
\[
{}y^{\prime } = \frac {4 t}{1+3 y^{2}}
\] |
[_separable] |
✓ |
1.240 |
|
|
\[
{}v^{\prime } = t^{2} v-2-2 v+t^{2}
\] |
[_separable] |
✓ |
1.664 |
|
|
\[
{}y^{\prime } = \frac {1}{t y+t +y+1}
\] |
[_separable] |
✓ |
1.890 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{t} y}{1+y^{2}}
\] |
[_separable] |
✓ |
1.755 |
|
|
\[
{}y^{\prime } = y^{2}-4
\] |
[_quadrature] |
✓ |
3.743 |
|
|
\[
{}w^{\prime } = \frac {w}{t}
\] |
[_separable] |
✓ |
1.635 |
|
|
\[
{}y^{\prime } = \sec \left (y\right )
\] |
[_quadrature] |
✓ |
2.011 |
|
|
\[
{}x^{\prime } = -t x
\] |
[_separable] |
✓ |
3.052 |
|
|
\[
{}y^{\prime } = t y
\] |
[_separable] |
✓ |
2.918 |
|
|
\[
{}y^{\prime } = -y^{2}
\] |
[_quadrature] |
✓ |
4.193 |
|
|
\[
{}y^{\prime } = t^{2} y^{3}
\] |
[_separable] |
✓ |
3.556 |
|
|
\[
{}y^{\prime } = -y^{2}
\] |
[_quadrature] |
✓ |
1.936 |
|
|
\[
{}y^{\prime } = \frac {t}{y-t^{2} y}
\] |
[_separable] |
✓ |
7.588 |
|
|
\[
{}y^{\prime } = 2 y+1
\] |
[_quadrature] |
✓ |
1.911 |
|
|
\[
{}y^{\prime } = t y^{2}+2 y^{2}
\] |
[_separable] |
✓ |
2.322 |
|
|
\[
{}x^{\prime } = \frac {t^{2}}{x+t^{3} x}
\] |
[_separable] |
✓ |
3.057 |
|
|
\[
{}y^{\prime } = \frac {1-y^{2}}{y}
\] |
[_quadrature] |
✓ |
7.217 |
|
|
\[
{}y^{\prime } = \left (1+y^{2}\right ) t
\] |
[_separable] |
✓ |
2.593 |
|
|
\[
{}y^{\prime } = \frac {1}{2 y+3}
\] |
[_quadrature] |
✓ |
2.121 |
|
|
\[
{}y^{\prime } = 2 t y^{2}+3 t^{2} y^{2}
\] |
[_separable] |
✓ |
2.194 |
|
|
\[
{}y^{\prime } = \frac {y^{2}+5}{y}
\] |
[_quadrature] |
✓ |
4.366 |
|
|
\[
{}y^{\prime } = t^{2}+t
\] |
[_quadrature] |
✓ |
0.455 |
|
|
\[
{}y^{\prime } = t^{2}+1
\] |
[_quadrature] |
✓ |
0.436 |
|
|
\[
{}y^{\prime } = 1-2 y
\] |
[_quadrature] |
✓ |
1.642 |
|
|
\[
{}y^{\prime } = 4 y^{2}
\] |
[_quadrature] |
✓ |
1.982 |
|
|
\[
{}y^{\prime } = 2 y \left (1-y\right )
\] |
[_quadrature] |
✓ |
2.407 |
|
|
\[
{}y^{\prime } = y+t +1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.260 |
|
|
\[
{}y^{\prime } = 3 y \left (1-y\right )
\] |
[_quadrature] |
✓ |
2.798 |
|
|
\[
{}y^{\prime } = 2 y-t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.527 |
|
|
\[
{}y^{\prime } = \left (y+\frac {1}{2}\right ) \left (y+t \right )
\] |
[_Riccati] |
✓ |
1.783 |
|
|
\[
{}y^{\prime } = \left (t +1\right ) y
\] |
[_separable] |
✓ |
3.026 |
|
|
\[
{}S^{\prime } = S^{3}-2 S^{2}+S
\] |
[_quadrature] |
✓ |
17.293 |
|
|
\[
{}S^{\prime } = S^{3}-2 S^{2}+S
\] |
[_quadrature] |
✓ |
16.936 |
|
|
\[
{}S^{\prime } = S^{3}-2 S^{2}+S
\] |
[_quadrature] |
✓ |
18.758 |
|
|
\[
{}S^{\prime } = S^{3}-2 S^{2}+S
\] |
[_quadrature] |
✓ |
18.585 |
|
|
\[
{}S^{\prime } = S^{3}-2 S^{2}+S
\] |
[_quadrature] |
✓ |
17.342 |
|
|
\[
{}y^{\prime } = y^{2}+y
\] |
[_quadrature] |
✓ |
2.202 |
|
|
\[
{}y^{\prime } = y^{2}-y
\] |
[_quadrature] |
✓ |
1.977 |
|
|
\[
{}y^{\prime } = y^{3}+y^{2}
\] |
[_quadrature] |
✓ |
17.349 |
|
|
\[
{}y^{\prime } = -t^{2}+2
\] |
[_quadrature] |
✓ |
0.458 |
|
|
\[
{}y^{\prime } = t y+t y^{2}
\] |
[_separable] |
✓ |
2.270 |
|
|
\[
{}y^{\prime } = t^{2}+t^{2} y
\] |
[_separable] |
✓ |
1.504 |
|
|
\[
{}y^{\prime } = t +t y
\] |
[_separable] |
✓ |
1.484 |
|
|
\[
{}y^{\prime } = t^{2}-2
\] |
[_quadrature] |
✓ |
0.514 |
|
|
\[
{}\theta ^{\prime } = \frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10}
\] |
[_quadrature] |
✓ |
35.954 |
|
|
\[
{}\theta ^{\prime } = 2
\] |
[_quadrature] |
✓ |
0.812 |
|
|
\[
{}\theta ^{\prime } = \frac {11}{10}-\frac {9 \cos \left (\theta \right )}{10}
\] |
[_quadrature] |
✓ |
35.741 |
|
|
\[
{}v^{\prime } = -\frac {v}{R C}
\] |
[_quadrature] |
✓ |
1.062 |
|
|
\[
{}v^{\prime } = \frac {K -v}{R C}
\] |
[_quadrature] |
✓ |
0.948 |
|
|
\[
{}v^{\prime } = 2 V \left (t \right )-2 v
\] |
[[_linear, ‘class A‘]] |
✓ |
1.072 |
|
|
\[
{}y^{\prime } = 2 y+1
\] |
[_quadrature] |
✓ |
2.056 |
|
|
\[
{}y^{\prime } = t -y^{2}
\] |
[[_Riccati, _special]] |
✓ |
2.157 |
|
|
\[
{}y^{\prime } = y^{2}-4 t
\] |
[[_Riccati, _special]] |
✓ |
2.262 |
|
|
\[
{}y^{\prime } = \sin \left (y\right )
\] |
[_quadrature] |
✓ |
32.553 |
|
|
\[
{}w^{\prime } = \left (3-w\right ) \left (w+1\right )
\] |
[_quadrature] |
✓ |
2.422 |
|
|
\[
{}w^{\prime } = \left (3-w\right ) \left (w+1\right )
\] |
[_quadrature] |
✓ |
2.436 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{\frac {2}{y}}
\] |
[_quadrature] |
✓ |
1.733 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{\frac {2}{y}}
\] |
[_quadrature] |
✓ |
1.770 |
|
|
\[
{}y^{\prime } = y^{2}-y^{3}
\] |
[_quadrature] |
✓ |
16.481 |
|
|
\[
{}y^{\prime } = 2 y^{3}+t^{2}
\] |
[_Abel] |
✗ |
0.771 |
|
|
\[
{}y^{\prime } = \sqrt {y}
\] |
[_quadrature] |
✓ |
1.732 |
|
|
\[
{}y^{\prime } = 2-y
\] |
[_quadrature] |
✓ |
1.878 |
|
|
\[
{}\theta ^{\prime } = \frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10}
\] |
[_quadrature] |
✓ |
1647.895 |
|
|
\[
{}y^{\prime } = y \left (y-1\right ) \left (y-3\right )
\] |
[_quadrature] |
✓ |
38.355 |
|
|
\[
{}y^{\prime } = y \left (y-1\right ) \left (y-3\right )
\] |
[_quadrature] |
✓ |
5.095 |
|