|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.257 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = x \,{\mathrm e}^{x}-3 x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.249 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime } = x \,{\mathrm e}^{x}-3 x^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.269 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x}
\] |
[_quadrature] |
✓ |
0.275 |
|
|
\[
{}y^{\prime }-y = 2 \,{\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.296 |
|
|
\[
{}y^{\prime \prime }-9 y = x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.297 |
|
|
\[
{}y^{\prime \prime }+9 y = x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.349 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+6 y = -2 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.599 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = -x^{2}+1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.326 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = x +\cos \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.406 |
|
|
\[
{}y^{\prime }-2 y = 6
\] |
[_quadrature] |
✓ |
0.317 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.309 |
|
|
\[
{}y^{\prime \prime }+9 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.290 |
|
|
\[
{}y^{\prime \prime }+9 y = 18 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.333 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.247 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.302 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.326 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.397 |
|
|
\[
{}y^{\prime }+2 y = \left \{\begin {array}{cc} 2 & 0\le x <1 \\ 1 & 1\le x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.528 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & 2\le x <4 \\ 0 & \operatorname {otherwise} \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.607 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ \left (x -1\right )^{2} & 1\le x \end {array}\right .
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.581 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ x^{2}-2 x +3 & 1\le x \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.666 |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le x <\pi \\ -\sin \left (3 x \right ) & \pi \le x \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.174 |
|
|
\[
{}y^{\prime \prime }-4 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.747 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.783 |
|
|
\[
{}y^{\prime }+3 y = \delta \left (-2+x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.411 |
|
|
\[
{}y^{\prime }-3 y = \delta \left (x -1\right )+2 \operatorname {Heaviside}\left (-2+x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.554 |
|
|
\[
{}y^{\prime \prime }+9 y = \delta \left (x -\pi \right )+\delta \left (x -3 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.592 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 \delta \left (x -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.394 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = \cos \left (x \right )+2 \delta \left (x -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.156 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (x \right ) \delta \left (x -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.498 |
|
|
\[
{}y^{\prime \prime }+a^{2} y = \delta \left (x -\pi \right ) f \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.353 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-3 y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.352 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}-2 y_{2} \\ y_{2}^{\prime }=y_{1}+3 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.422 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+2 y_{2}+x -1 \\ y_{2}^{\prime }=3 y_{1}+2 y_{2}-5 x -2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.655 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=\frac {2 y_{1}}{x}-\frac {y_{2}}{x^{2}}-3+\frac {1}{x}-\frac {1}{x^{2}} \\ y_{2}^{\prime }=2 y_{1}+1-6 x \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.055 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x \\ y_{2}^{\prime }=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.056 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}-2 y_{2} \\ y_{2}^{\prime }=y_{2}-y_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.707 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right ) \\ y_{2}^{\prime }=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1 \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.058 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right ) \\ y_{2}^{\prime }=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1 \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.059 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }={\mathrm e}^{-x} y_{1}-\sqrt {x +1}\, y_{2}+x^{2} \\ y_{2}^{\prime }=\frac {y_{1}}{\left (-2+x \right )^{2}} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.059 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }={\mathrm e}^{-x} y_{1}-\sqrt {x +1}\, y_{2}+x^{2} \\ y_{2}^{\prime }=\frac {y_{1}}{\left (-2+x \right )^{2}} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.060 |
|
|
\(\left [\begin {array}{cc} -2 & -4 \\ 1 & 3 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.154 |
|
|
\(\left [\begin {array}{cc} -3 & -1 \\ 2 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.204 |
|
|
\(\left [\begin {array}{ccc} 1 & 0 & 1 \\ 0 & 1 & -1 \\ -2 & 0 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.296 |
|
|
\(\left [\begin {array}{ccc} 3 & 1 & -1 \\ 1 & 3 & -1 \\ 3 & 3 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.217 |
|
|
\(\left [\begin {array}{ccc} 7 & -1 & 6 \\ -10 & 4 & -12 \\ -2 & 1 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.266 |
|
|
\(\left [\begin {array}{cccc} 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.270 |
|
|
\(\left [\begin {array}{cccc} 1 & 3 & 5 & 7 \\ 2 & 6 & 10 & 14 \\ 3 & 9 & 15 & 21 \\ 6 & 18 & 30 & 42 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.283 |
|
|
\(\left [\begin {array}{ccccc} 1 & 3 & 5 & 2 & 4 \\ 5 & 2 & 4 & 1 & 3 \\ 4 & 1 & 3 & 5 & 2 \\ 3 & 5 & 2 & 4 & 1 \\ 2 & 4 & 1 & 3 & 5 \end {array}\right ]\) |
Eigenvectors |
✓ |
4.802 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-3 y_{2}+5 \,{\mathrm e}^{x} \\ y_{2}^{\prime }=y_{1}+4 y_{2}-2 \,{\mathrm e}^{-x} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.336 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2}-2 y_{1}+\sin \left (2 x \right ) \\ y_{2}^{\prime }=-3 y_{1}+y_{2}-2 \cos \left (3 x \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
2.875 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{2} \\ y_{2}^{\prime }=3 y_{1} \\ y_{3}^{\prime }=2 y_{3}-y_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.645 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 x y_{1}-x^{2} y_{2}+4 x \\ y_{2}^{\prime }={\mathrm e}^{x} y_{1}+3 \,{\mathrm e}^{-x} y_{2}-\cos \left (3 x \right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.059 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-3 y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.337 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-3 y_{2}+4 x -2 \\ y_{2}^{\prime }=y_{1}-2 y_{2}+3 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.507 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x} \\ y_{2}^{\prime }=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.052 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x \\ y_{2}^{\prime }=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.053 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}+y_{2}-2 y_{3} \\ y_{2}^{\prime }=3 y_{2}-2 y_{3} \\ y_{3}^{\prime }=3 y_{1}+y_{2}-3 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.493 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=5 y_{1}-5 y_{2}-5 y_{3} \\ y_{2}^{\prime }=-y_{1}+4 y_{2}+2 y_{3} \\ y_{3}^{\prime }=3 y_{1}-5 y_{2}-3 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.654 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}+6 y_{2}+6 y_{3} \\ y_{2}^{\prime }=y_{1}+3 y_{2}+2 y_{3} \\ y_{3}^{\prime }=-y_{1}-4 y_{2}-3 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.512 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+2 y_{2}-3 y_{3} \\ y_{2}^{\prime }=-3 y_{1}+4 y_{2}-2 y_{3} \\ y_{3}^{\prime }=2 y_{1}+y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.750 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-2 y_{1}-y_{2}+y_{3} \\ y_{2}^{\prime }=-y_{1}-2 y_{2}-y_{3} \\ y_{3}^{\prime }=y_{1}-y_{2}-2 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.359 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+y_{2}+2 y_{3} \\ y_{2}^{\prime }=y_{1}+y_{2}+2 y_{3} \\ y_{3}^{\prime }=2 y_{1}+2 y_{2}+4 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.352 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}+y_{2} \\ y_{2}^{\prime }=-y_{1}+2 y_{2} \\ y_{3}^{\prime }=3 y_{3}-4 y_{4} \\ y_{4}^{\prime }=4 y_{3}+3 y_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.825 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2} \\ y_{2}^{\prime }=-3 y_{1}+2 y_{3} \\ y_{3}^{\prime }=y_{4} \\ y_{4}^{\prime }=2 y_{1}-5 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
4.716 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+2 y_{2} \\ y_{2}^{\prime }=3 y_{2}-2 y_{1} \\ y_{3}^{\prime }=y_{3} \\ y_{4}^{\prime }=2 y_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.643 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2}+y_{4} \\ y_{2}^{\prime }=y_{1}-y_{3} \\ y_{3}^{\prime }=y_{4} \\ y_{4}^{\prime }=y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.506 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+3 y \\ y^{\prime }=-x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.328 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=-2 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.301 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.623 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=5 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.418 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.394 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.372 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x-y+2 \\ y^{\prime }=3 x-y-3 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.558 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y-6 \\ y^{\prime }=4 x-y+2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.788 |
|
|
\[
{}y^{\prime } = \frac {y+1}{t +1}
\] |
[_separable] |
✓ |
1.417 |
|
|
\[
{}y^{\prime } = t^{2} y^{2}
\] |
[_separable] |
✓ |
1.684 |
|
|
\[
{}y^{\prime } = t^{4} y
\] |
[_separable] |
✓ |
1.158 |
|
|
\[
{}y^{\prime } = 2 y+1
\] |
[_quadrature] |
✓ |
0.923 |
|
|
\[
{}y^{\prime } = 2-y
\] |
[_quadrature] |
✓ |
0.944 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-y}
\] |
[_quadrature] |
✓ |
0.956 |
|
|
\[
{}x^{\prime } = 1+x^{2}
\] |
[_quadrature] |
✓ |
0.962 |
|
|
\[
{}y^{\prime } = 2 t y^{2}+3 y^{2}
\] |
[_separable] |
✓ |
1.476 |
|
|
\[
{}y^{\prime } = \frac {t}{y}
\] |
[_separable] |
✓ |
2.985 |
|
|
\[
{}y^{\prime } = \frac {t}{t^{2} y+y}
\] |
[_separable] |
✓ |
1.254 |
|
|
\[
{}y^{\prime } = t y^{{1}/{3}}
\] |
[_separable] |
✓ |
3.873 |
|
|
\[
{}y^{\prime } = \frac {1}{2 y+1}
\] |
[_quadrature] |
✓ |
0.974 |
|
|
\[
{}y^{\prime } = \frac {2 y+1}{t}
\] |
[_separable] |
✓ |
1.651 |
|
|
\[
{}y^{\prime } = y \left (1-y\right )
\] |
[_quadrature] |
✓ |
1.623 |
|
|
\[
{}y^{\prime } = \frac {4 t}{1+3 y^{2}}
\] |
[_separable] |
✓ |
1.058 |
|
|
\[
{}v^{\prime } = t^{2} v-2-2 v+t^{2}
\] |
[_separable] |
✓ |
1.312 |
|
|
\[
{}y^{\prime } = \frac {1}{t y+t +y+1}
\] |
[_separable] |
✓ |
1.309 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{t} y}{1+y^{2}}
\] |
[_separable] |
✓ |
1.497 |
|
|
\[
{}y^{\prime } = y^{2}-4
\] |
[_quadrature] |
✓ |
1.362 |
|
|
\[
{}w^{\prime } = \frac {w}{t}
\] |
[_separable] |
✓ |
1.237 |
|
|
\[
{}y^{\prime } = \sec \left (y\right )
\] |
[_quadrature] |
✓ |
0.934 |
|
|
\[
{}x^{\prime } = -x t
\] |
[_separable] |
✓ |
1.889 |
|
|
\[
{}y^{\prime } = t y
\] |
[_separable] |
✓ |
1.583 |
|
|
\[
{}y^{\prime } = -y^{2}
\] |
[_quadrature] |
✓ |
1.187 |
|