|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.458 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.439 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.466 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.468 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.451 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.454 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.451 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.431 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.505 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.419 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=-4 x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.461 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-5 y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.713 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.748 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-6 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.720 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+4 y \\ y^{\prime }=-3 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.711 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.415 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=-4 x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.468 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-5 y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.718 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.723 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-6 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.717 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+4 y \\ y^{\prime }=-3 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.759 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {9 x}{10}-2 y \\ y^{\prime }=x+\frac {11 y}{10} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.549 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+10 y \\ y^{\prime }=-x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.383 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x \\ y^{\prime }=x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.428 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.648 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-y \\ y^{\prime }=x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.418 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.502 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x \\ y^{\prime }=x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.402 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.413 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-y \\ y^{\prime }=x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.506 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.425 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.408 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+4 y \\ y^{\prime }=3 x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.429 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+2 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.428 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.247 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 y \\ y^{\prime }=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.250 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-y \\ y^{\prime }=4 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.457 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }-7 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.858 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.838 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {y}{10} \\ y^{\prime }=\frac {z}{5} \\ z^{\prime }=\frac {2 x}{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.072 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x \\ z^{\prime }=2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.486 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+3 y \\ y^{\prime }=3 x-2 y \\ z^{\prime }=-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.383 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+3 z \\ y^{\prime }=-y \\ z^{\prime }=-3 x+z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.514 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=2 y-z \\ z^{\prime }=-y+2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.320 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=-2 y \\ z^{\prime }=-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.312 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=-2 y \\ z^{\prime }=z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.309 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=2 x-4 y \\ z^{\prime }=-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.392 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=2 x-4 y \\ z^{\prime }=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.319 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=-2 y+z \\ z^{\prime }=-2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.317 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=z \\ z^{\prime }=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.247 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=-2 y+3 z \\ z^{\prime }=-x+3 y-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.849 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+3 y \\ y^{\prime }=z-y \\ z^{\prime }=5 x-5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.741 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-10 x+10 y \\ y^{\prime }=28 x-y \\ z^{\prime }=-\frac {8 z}{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.664 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=z-y \\ y^{\prime }=z-x \\ z^{\prime }=z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.324 |
|
|
\(\left [\begin {array}{cc} 1 & 0 \\ 0 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.150 |
|
|
\(\left [\begin {array}{cc} 0 & 1 \\ 2 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.211 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.276 |
|
|
\(\left [\begin {array}{cc} 1 & 0 \\ 2 & 3 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.148 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=0 \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.292 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\pi ^{2} x+\frac {187 y}{5} \\ y^{\prime }=\sqrt {555}\, x+\frac {400617 y}{5000} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.916 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.398 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+y \\ y^{\prime }=y-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.544 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+y \\ y^{\prime }=-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.541 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.385 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.316 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+y \\ y^{\prime }=-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.543 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-4 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.323 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-3 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.656 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.120 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.602 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.208 |
|
|
\[
{}y^{\prime \prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
43.952 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.099 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \,{\mathrm e}^{-3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.069 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.053 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
11.030 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.179 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.105 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+4 y = {\mathrm e}^{4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.124 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 4 \,{\mathrm e}^{-3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.161 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.258 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+12 y = 3 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.372 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.953 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.685 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-\frac {t}{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.563 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.126 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.577 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-\frac {t}{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
12.142 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.397 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
12.712 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.020 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+4 y = 5
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.450 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.271 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+10 y = 10
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.667 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+6 y = -8
\] |
[[_2nd_order, _missing_x]] |
✓ |
8.392 |
|
|
\[
{}y^{\prime \prime }+9 y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.754 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.607 |
|
|
\[
{}y^{\prime \prime }+2 y = -3
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.537 |
|
|
\[
{}y^{\prime \prime }+4 y = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.515 |
|
|
\[
{}y^{\prime \prime }+9 y = 6
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.450 |
|