|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.457 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.224 |
|
|
\[
{}y y^{\prime }+y^{4} = \sin \left (x \right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
2.754 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+5 y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.161 |
|
|
\[
{}{y^{\prime }}^{2}+y = 0
\] |
[_quadrature] |
✓ |
0.349 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.447 |
|
|
\[
{}x {y^{\prime \prime }}^{2}+2 y = 2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.084 |
|
|
\[
{}x^{\prime \prime }+2 \sin \left (x\right ) = \sin \left (2 t \right )
\] |
[NONE] |
✗ |
0.999 |
|
|
\[
{}2 x -1-y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.465 |
|
|
\[
{}2 x -y-y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.903 |
|
|
\[
{}y^{\prime }+2 y = 0
\] |
[_quadrature] |
✓ |
1.788 |
|
|
\[
{}y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
1.684 |
|
|
\[
{}y^{\prime }+y = \sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.514 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.893 |
|
|
\[
{}y^{\prime \prime }+9 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.958 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }-10 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.148 |
|
|
\[
{}x^{\prime \prime }+x = t \cos \left (t \right )-\cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.674 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+40 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.716 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.048 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.049 |
|
|
\[
{}x^{2} y^{\prime \prime }-12 x y^{\prime }+42 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.003 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
4.552 |
|
|
\[
{}y^{\prime } = -\frac {x}{y}
\] |
[_separable] |
✓ |
4.292 |
|
|
\[
{}3 y \left (t^{2}+y\right )+t \left (t^{2}+6 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.783 |
|
|
\[
{}y^{\prime } = -\frac {2 y}{x}-3
\] |
[_linear] |
✓ |
2.808 |
|
|
\[
{}y \cos \left (t \right )+\left (2 y+\sin \left (t \right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.316 |
|
|
\[
{}\frac {y}{x}+\cos \left (y\right )+\left (\ln \left (x \right )-x \sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
6.743 |
|
|
\[
{}y^{\prime } = \left (x^{2}-1\right ) \left (x^{3}-3 x \right )^{3}
\] |
[_quadrature] |
✓ |
0.533 |
|
|
\[
{}y^{\prime } = x \sin \left (x^{2}\right )
\] |
[_quadrature] |
✓ |
0.536 |
|
|
\[
{}y^{\prime } = \frac {x}{\sqrt {x^{2}-16}}
\] |
[_quadrature] |
✓ |
0.254 |
|
|
\[
{}y^{\prime } = \frac {1}{\ln \left (x \right ) x}
\] |
[_quadrature] |
✓ |
0.427 |
|
|
\[
{}y^{\prime } = \ln \left (x \right ) x
\] |
[_quadrature] |
✓ |
0.432 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{-x}
\] |
[_quadrature] |
✓ |
0.569 |
|
|
\[
{}y^{\prime } = \frac {-2 x -10}{\left (x +2\right ) \left (x -4\right )}
\] |
[_quadrature] |
✓ |
0.612 |
|
|
\[
{}y^{\prime } = \frac {-x^{2}+x}{\left (x +1\right ) \left (x^{2}+1\right )}
\] |
[_quadrature] |
✓ |
0.653 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {x^{2}-16}}{x}
\] |
[_quadrature] |
✓ |
0.376 |
|
|
\[
{}y^{\prime } = \left (-x^{2}+4\right )^{{3}/{2}}
\] |
[_quadrature] |
✓ |
0.582 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}-16}
\] |
[_quadrature] |
✓ |
0.623 |
|
|
\[
{}y^{\prime } = \cos \left (x \right ) \cot \left (x \right )
\] |
[_quadrature] |
✓ |
0.679 |
|
|
\[
{}y^{\prime } = \sin \left (x \right )^{3} \tan \left (x \right )
\] |
[_quadrature] |
✓ |
0.735 |
|
|
\[
{}y^{\prime }+2 y = 0
\] |
[_quadrature] |
✓ |
3.374 |
|
|
\[
{}y^{\prime }+y = \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.819 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.480 |
|
|
\[
{}y^{\prime \prime }+9 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.358 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.130 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.127 |
|
|
\[
{}t^{2} y^{\prime \prime }-12 t y^{\prime }+42 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.904 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.852 |
|
|
\[
{}y^{\prime } = 4 x^{3}-x +2
\] |
[_quadrature] |
✓ |
0.729 |
|
|
\[
{}y^{\prime } = \sin \left (2 t \right )-\cos \left (2 t \right )
\] |
[_quadrature] |
✓ |
0.898 |
|
|
\[
{}y^{\prime } = \frac {\cos \left (\frac {1}{x}\right )}{x^{2}}
\] |
[_quadrature] |
✓ |
1.042 |
|
|
\[
{}y^{\prime } = \frac {\ln \left (x \right )}{x}
\] |
[_quadrature] |
✓ |
0.775 |
|
|
\[
{}y^{\prime } = \frac {\left (x -4\right ) y^{3}}{x^{3} \left (y-2\right )}
\] |
[_separable] |
✓ |
4.131 |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 x y}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
3.237 |
|
|
\[
{}x y^{\prime }+y = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.458 |
|
|
\[
{}16 y^{\prime \prime }+24 y^{\prime }+153 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.858 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 y \\ y^{\prime }=-x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.846 |
|
|
\[
{}4 x \left (x^{2}+y^{2}\right )-5 y+4 y \left (x^{2}+y^{2}-5 x \right ) y^{\prime } = 0
\] |
[_rational] |
✗ |
32.424 |
|
|
\[
{}y^{\prime } = \sin \left (x \right )^{4}
\] |
[_quadrature] |
✓ |
1.063 |
|
|
\[
{}y^{\prime \prime \prime \prime }+\frac {25 y^{\prime \prime }}{2}-5 y^{\prime }+\frac {629 y}{16} = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.123 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 y \\ y^{\prime }=-4 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.590 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x+4 y \\ y^{\prime }=2 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.636 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
2.144 |
|
|
\[
{}y^{\prime }-y = \sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.581 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.913 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+45 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.860 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }-16 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.139 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
4.008 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
12.949 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.032 |
|
|
\[
{}2 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.621 |
|
|
\[
{}y \cos \left (x y\right )+\sin \left (x \right )+x \cos \left (x y\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
36.377 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{-x^{2}}
\] |
[_quadrature] |
✓ |
0.510 |
|
|
\[
{}y^{\prime } = x^{2} \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.640 |
|
|
\[
{}y^{\prime } = \frac {2 x^{2}-x +1}{\left (-1+x \right ) \left (x^{2}+1\right )}
\] |
[_quadrature] |
✓ |
0.625 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{\sqrt {x^{2}-1}}
\] |
[_quadrature] |
✓ |
0.351 |
|
|
\[
{}y^{\prime }+2 y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.685 |
|
|
\[
{}y^{\prime \prime }+4 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.397 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.465 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )^{2} \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.837 |
|
|
\[
{}y^{\prime } = \frac {4 x -9}{3 \left (x -3\right )^{{2}/{3}}}
\] |
[_quadrature] |
✓ |
0.556 |
|
|
\[
{}y^{\prime }+t^{2} = y^{2}
\] |
[_Riccati] |
✓ |
1.640 |
|
|
\[
{}y^{\prime }+t^{2} = \frac {1}{y^{2}}
\] |
[_rational] |
✗ |
0.819 |
|
|
\[
{}y^{\prime } = y+\frac {1}{-t +1}
\] |
[_linear] |
✓ |
1.454 |
|
|
\[
{}y^{\prime } = y^{{1}/{5}}
\] |
[_quadrature] |
✓ |
3.035 |
|
|
\[
{}\frac {y^{\prime }}{t} = \sqrt {y}
\] |
[_separable] |
✓ |
6.648 |
|
|
\[
{}y^{\prime } = 4 t^{2}-t y^{2}
\] |
[_Riccati] |
✓ |
2.817 |
|
|
\[
{}y^{\prime } = y \sqrt {t}
\] |
[_separable] |
✓ |
1.660 |
|
|
\[
{}y^{\prime } = 6 y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
2.232 |
|
|
\[
{}t y^{\prime } = y
\] |
[_separable] |
✓ |
1.724 |
|
|
\[
{}y^{\prime } = y \tan \left (t \right )
\] |
[_separable] |
✓ |
2.445 |
|
|
\[
{}y^{\prime } = \frac {1}{t^{2}+1}
\] |
[_quadrature] |
✓ |
0.778 |
|
|
\[
{}y^{\prime } = \sqrt {-1+y^{2}}
\] |
[_quadrature] |
✓ |
83.408 |
|
|
\[
{}y^{\prime } = \sqrt {-1+y^{2}}
\] |
[_quadrature] |
✓ |
4.666 |
|
|
\[
{}y^{\prime } = \sqrt {-1+y^{2}}
\] |
[_quadrature] |
✓ |
28.865 |
|
|
\[
{}y^{\prime } = \sqrt {-1+y^{2}}
\] |
[_quadrature] |
✓ |
4.543 |
|
|
\[
{}y^{\prime } = \sqrt {25-y^{2}}
\] |
[_quadrature] |
✓ |
1038.546 |
|
|
\[
{}y^{\prime } = \sqrt {25-y^{2}}
\] |
[_quadrature] |
✓ |
6.530 |
|
|
\[
{}y^{\prime } = \sqrt {25-y^{2}}
\] |
[_quadrature] |
✓ |
288.201 |
|
|
\[
{}y^{\prime } = \sqrt {25-y^{2}}
\] |
[_quadrature] |
✓ |
6.736 |
|