|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 y^{\prime } x -y = 2 x \cos \left (x \right )
\] |
[_linear] |
✓ |
1.596 |
|
|
\[
{}x y+x^{2} y^{\prime } = 10 \sin \left (x \right )
\] |
[_linear] |
✓ |
1.413 |
|
|
\[
{}y^{\prime }+2 x y = 1
\] |
[_linear] |
✓ |
0.946 |
|
|
\[
{}y^{\prime } x -2 y = 0
\] |
[_separable] |
✓ |
1.526 |
|
|
\[
{}y^{\prime } = -\frac {x}{y}
\] |
[_separable] |
✓ |
3.139 |
|
|
\[
{}2 y+y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.825 |
|
|
\[
{}5 y^{\prime } = 2 y
\] |
[_quadrature] |
✓ |
0.753 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.341 |
|
|
\[
{}2 y^{\prime \prime }+7 y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.337 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.891 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.417 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.930 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }-3 x y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.231 |
|
|
\[
{}3 y^{\prime } x +5 y = 10
\] |
[_separable] |
✓ |
1.768 |
|
|
\[
{}y^{\prime } = y^{2}+2 y-3
\] |
[_quadrature] |
✓ |
0.846 |
|
|
\[
{}\left (-1+y\right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.941 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+6 y = 10
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.622 |
|
|
\[
{}{y^{\prime }}^{2} = 4 y
\] |
[_quadrature] |
✓ |
0.447 |
|
|
\[
{}{y^{\prime }}^{2} = 9-y^{2}
\] |
[_quadrature] |
✓ |
0.922 |
|
|
\[
{}y y^{\prime }+\sqrt {16-y^{2}} = 0
\] |
[_quadrature] |
✓ |
2.614 |
|
|
\[
{}{y^{\prime }}^{2}-2 y^{\prime }+4 y = 4 x -1
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.529 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+3 y \\ y^{\prime }=5 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.424 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=4 y+{\mathrm e}^{t} \\ y^{\prime \prime }=4 x-{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.051 |
|
|
\[
{}y^{\prime } = \sqrt {1-y^{2}}
\] |
[_quadrature] |
✓ |
44.960 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+4 y = 5 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.720 |
|
|
\[
{}y^{\prime } = f \left (x \right )
\] |
[_quadrature] |
✓ |
0.268 |
|
|
\[
{}y^{\prime \prime } = f \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.607 |
|
|
\[
{}x {y^{\prime }}^{2}-4 y^{\prime }-12 x^{3} = 0
\] |
[_quadrature] |
✓ |
0.358 |
|
|
\[
{}y^{\prime } = 5-y
\] |
[_quadrature] |
✓ |
0.610 |
|
|
\[
{}y^{\prime } = 4+y^{2}
\] |
[_quadrature] |
✓ |
8.174 |
|
|
\[
{}y^{\prime \prime \prime \prime }-20 y^{\prime \prime \prime }+158 y^{\prime \prime }-580 y^{\prime }+841 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.099 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+20 y^{\prime } x -78 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.146 |
|
|
\[
{}y^{\prime } = y-y^{2}
\] |
[_quadrature] |
✓ |
1.332 |
|
|
\[
{}y^{\prime } = y-y^{2}
\] |
[_quadrature] |
✓ |
1.321 |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
1.949 |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
1.969 |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
2.036 |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
1.984 |
|
|
\[
{}x^{\prime \prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
24.052 |
|
|
\[
{}x^{\prime \prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.262 |
|
|
\[
{}x^{\prime \prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.823 |
|
|
\[
{}x^{\prime \prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.921 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.770 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.576 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.431 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.430 |
|
|
\[
{}y^{\prime } = 3 y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
1.544 |
|
|
\[
{}y^{\prime } x = 2 y
\] |
[_separable] |
✓ |
1.804 |
|
|
\[
{}y^{\prime } = y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
1.062 |
|
|
\[
{}y^{\prime } = \sqrt {x y}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
9.018 |
|
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
1.271 |
|
|
\[
{}y^{\prime }-y = x
\] |
[[_linear, ‘class A‘]] |
✓ |
0.929 |
|
|
\[
{}\left (4-y^{2}\right ) y^{\prime } = x^{2}
\] |
[_separable] |
✓ |
1.252 |
|
|
\[
{}\left (y^{3}+1\right ) y^{\prime } = x^{2}
\] |
[_separable] |
✓ |
1.255 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.188 |
|
|
\[
{}\left (y-x \right ) y^{\prime } = x +y
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.923 |
|
|
\[
{}y^{\prime } = \sqrt {y^{2}-9}
\] |
[_quadrature] |
✓ |
24.040 |
|
|
\[
{}y^{\prime } = \sqrt {y^{2}-9}
\] |
[_quadrature] |
✓ |
3.329 |
|
|
\[
{}y^{\prime } = \sqrt {y^{2}-9}
\] |
[_quadrature] |
✓ |
3.545 |
|
|
\[
{}y^{\prime } = \sqrt {y^{2}-9}
\] |
[_quadrature] |
✓ |
9.648 |
|
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
1.501 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
1.631 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.345 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.589 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.266 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.384 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.321 |
|
|
\[
{}y y^{\prime } = 3 x
\] |
[_separable] |
✓ |
3.363 |
|
|
\[
{}y y^{\prime } = 3 x
\] |
[_separable] |
✓ |
3.156 |
|
|
\[
{}y y^{\prime } = 3 x
\] |
[_separable] |
✓ |
6.608 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.948 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.259 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.272 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.606 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.220 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.959 |
|
|
\[
{}y^{\prime } = x -2 y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.207 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✗ |
1.985 |
|
|
\[
{}2 y^{\prime \prime }-3 y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.341 |
|
|
\[
{}2 y+y^{\prime } = 3 x -6
\] |
[[_linear, ‘class A‘]] |
✓ |
0.978 |
|
|
\[
{}y^{\prime } = x \sqrt {y}
\] |
[_separable] |
✓ |
5.470 |
|
|
\[
{}y^{\prime } x = 2 x
\] |
[_quadrature] |
✓ |
0.576 |
|
|
\[
{}y^{\prime } = 2
\] |
[_quadrature] |
✓ |
0.620 |
|
|
\[
{}y^{\prime } = 2 y-4
\] |
[_quadrature] |
✓ |
0.660 |
|
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
1.283 |
|
|
\[
{}y^{\prime \prime }+9 y = 18
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.600 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.953 |
|
|
\[
{}y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.749 |
|
|
\[
{}y^{\prime } = y \left (y-3\right )
\] |
[_quadrature] |
✓ |
1.049 |
|
|
\[
{}3 y^{\prime } x -2 y = 0
\] |
[_separable] |
✓ |
1.575 |
|
|
\[
{}\left (-2+2 y\right ) y^{\prime } = 2 x -1
\] |
[_separable] |
✓ |
3.188 |
|
|
\[
{}y^{\prime } x +y = 2 x
\] |
[_linear] |
✓ |
2.263 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.900 |
|
|
\[
{}{y^{\prime }}^{2} = 4 x^{2}
\] |
[_quadrature] |
✓ |
0.358 |
|
|
\[
{}y^{\prime } = 6 \sqrt {y}+5 x^{3}
\] |
[_Chini] |
✗ |
1.349 |
|
|
\[
{}y^{\prime \prime }+y = 2 \cos \left (x \right )-2 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.937 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.732 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.903 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = \sec \left (\ln \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.544 |
|
|
\[
{}y^{\prime }+y \sin \left (x \right ) = x
\] |
[_linear] |
✓ |
1.713 |
|