|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.264 |
|
|
\[
{}y^{\prime } = -\frac {x}{y}
\] |
[_separable] |
✓ |
3.331 |
|
|
\[
{}3 y \left (t^{2}+y\right )+t \left (t^{2}+6 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.891 |
|
|
\[
{}y^{\prime } = -\frac {2 y}{x}-3
\] |
[_linear] |
✓ |
2.419 |
|
|
\[
{}y \cos \left (t \right )+\left (2 y+\sin \left (t \right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.931 |
|
|
\[
{}\frac {y}{x}+\cos \left (y\right )+\left (\ln \left (x \right )-x \sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
4.806 |
|
|
\[
{}y^{\prime } = \left (x^{2}-1\right ) \left (x^{3}-3 x \right )^{3}
\] |
[_quadrature] |
✓ |
0.521 |
|
|
\[
{}y^{\prime } = x \sin \left (x^{2}\right )
\] |
[_quadrature] |
✓ |
0.528 |
|
|
\[
{}y^{\prime } = \frac {x}{\sqrt {x^{2}-16}}
\] |
[_quadrature] |
✓ |
0.240 |
|
|
\[
{}y^{\prime } = \frac {1}{x \ln \left (x \right )}
\] |
[_quadrature] |
✓ |
0.417 |
|
|
\[
{}y^{\prime } = x \ln \left (x \right )
\] |
[_quadrature] |
✓ |
0.441 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{-x}
\] |
[_quadrature] |
✓ |
0.504 |
|
|
\[
{}y^{\prime } = \frac {-2 x -10}{\left (x +2\right ) \left (x -4\right )}
\] |
[_quadrature] |
✓ |
0.530 |
|
|
\[
{}y^{\prime } = \frac {-x^{2}+x}{\left (x +1\right ) \left (x^{2}+1\right )}
\] |
[_quadrature] |
✓ |
0.583 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {x^{2}-16}}{x}
\] |
[_quadrature] |
✓ |
0.333 |
|
|
\[
{}y^{\prime } = \left (-x^{2}+4\right )^{{3}/{2}}
\] |
[_quadrature] |
✓ |
0.495 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}-16}
\] |
[_quadrature] |
✓ |
0.568 |
|
|
\[
{}y^{\prime } = \cos \left (x \right ) \cot \left (x \right )
\] |
[_quadrature] |
✓ |
0.598 |
|
|
\[
{}y^{\prime } = \sin \left (x \right )^{3} \tan \left (x \right )
\] |
[_quadrature] |
✓ |
0.722 |
|
|
\[
{}y^{\prime }+2 y = 0
\] |
[_quadrature] |
✓ |
1.778 |
|
|
\[
{}y^{\prime }+y = \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.619 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.692 |
|
|
\[
{}y^{\prime \prime }+9 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.765 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.141 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.142 |
|
|
\[
{}t^{2} y^{\prime \prime }-12 t y^{\prime }+42 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.967 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.937 |
|
|
\[
{}y^{\prime } = 4 x^{3}-x +2
\] |
[_quadrature] |
✓ |
0.627 |
|
|
\[
{}y^{\prime } = \sin \left (2 t \right )-\cos \left (2 t \right )
\] |
[_quadrature] |
✓ |
0.864 |
|
|
\[
{}y^{\prime } = \frac {\cos \left (\frac {1}{x}\right )}{x^{2}}
\] |
[_quadrature] |
✓ |
0.912 |
|
|
\[
{}y^{\prime } = \frac {\ln \left (x \right )}{x}
\] |
[_quadrature] |
✓ |
0.697 |
|
|
\[
{}y^{\prime } = \frac {\left (x -4\right ) y^{3}}{x^{3} \left (y-2\right )}
\] |
[_separable] |
✓ |
3.073 |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 x y}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.834 |
|
|
\[
{}y^{\prime } x +y = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.299 |
|
|
\[
{}16 y^{\prime \prime }+24 y^{\prime }+153 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.100 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 y \\ y^{\prime }=-x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.712 |
|
|
\[
{}4 x \left (x^{2}+y^{2}\right )-5 y+4 y \left (x^{2}+y^{2}-5 x \right ) y^{\prime } = 0
\] |
[_rational] |
✗ |
32.020 |
|
|
\[
{}y^{\prime } = \sin \left (x \right )^{4}
\] |
[_quadrature] |
✓ |
0.917 |
|
|
\[
{}y^{\prime \prime \prime \prime }+\frac {25 y^{\prime \prime }}{2}-5 y^{\prime }+\frac {629 y}{16} = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.104 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 y \\ y^{\prime }=-4 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.493 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x+4 y \\ y^{\prime }=2 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.610 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
1.813 |
|
|
\[
{}y^{\prime }-y = \sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.303 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.054 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+45 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.006 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x -16 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.336 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.852 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
7.612 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.197 |
|
|
\[
{}2 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.325 |
|
|
\[
{}y \cos \left (x y\right )+\sin \left (x \right )+x \cos \left (x y\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
35.405 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{-x^{2}}
\] |
[_quadrature] |
✓ |
0.504 |
|
|
\[
{}y^{\prime } = x^{2} \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.548 |
|
|
\[
{}y^{\prime } = \frac {2 x^{2}-x +1}{\left (x -1\right ) \left (x^{2}+1\right )}
\] |
[_quadrature] |
✓ |
0.557 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{\sqrt {x^{2}-1}}
\] |
[_quadrature] |
✓ |
0.289 |
|
|
\[
{}y^{\prime }+2 y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.531 |
|
|
\[
{}y^{\prime \prime }+4 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.559 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.601 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )^{2} \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.790 |
|
|
\[
{}y^{\prime } = \frac {4 x -9}{3 \left (x -3\right )^{{2}/{3}}}
\] |
[_quadrature] |
✓ |
0.504 |
|
|
\[
{}y^{\prime }+t^{2} = y^{2}
\] |
[_Riccati] |
✓ |
1.461 |
|
|
\[
{}y^{\prime }+t^{2} = \frac {1}{y^{2}}
\] |
[_rational] |
✗ |
0.698 |
|
|
\[
{}y^{\prime } = y+\frac {1}{-t +1}
\] |
[_linear] |
✓ |
1.279 |
|
|
\[
{}y^{\prime } = y^{{1}/{5}}
\] |
[_quadrature] |
✓ |
1.529 |
|
|
\[
{}\frac {y^{\prime }}{t} = \sqrt {y}
\] |
[_separable] |
✓ |
4.333 |
|
|
\[
{}y^{\prime } = 4 t^{2}-t y^{2}
\] |
[_Riccati] |
✓ |
2.400 |
|
|
\[
{}y^{\prime } = y \sqrt {t}
\] |
[_separable] |
✓ |
1.454 |
|
|
\[
{}y^{\prime } = 6 y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
1.732 |
|
|
\[
{}t y^{\prime } = y
\] |
[_separable] |
✓ |
1.606 |
|
|
\[
{}y^{\prime } = y \tan \left (t \right )
\] |
[_separable] |
✓ |
2.221 |
|
|
\[
{}y^{\prime } = \frac {1}{t^{2}+1}
\] |
[_quadrature] |
✓ |
0.699 |
|
|
\[
{}y^{\prime } = \sqrt {y^{2}-1}
\] |
[_quadrature] |
✓ |
10.246 |
|
|
\[
{}y^{\prime } = \sqrt {y^{2}-1}
\] |
[_quadrature] |
✓ |
7.036 |
|
|
\[
{}y^{\prime } = \sqrt {y^{2}-1}
\] |
[_quadrature] |
✓ |
10.683 |
|
|
\[
{}y^{\prime } = \sqrt {y^{2}-1}
\] |
[_quadrature] |
✓ |
4.732 |
|
|
\[
{}y^{\prime } = \sqrt {25-y^{2}}
\] |
[_quadrature] |
✓ |
283.710 |
|
|
\[
{}y^{\prime } = \sqrt {25-y^{2}}
\] |
[_quadrature] |
✓ |
3.014 |
|
|
\[
{}y^{\prime } = \sqrt {25-y^{2}}
\] |
[_quadrature] |
✓ |
7.507 |
|
|
\[
{}y^{\prime } = \sqrt {25-y^{2}}
\] |
[_quadrature] |
✓ |
41.872 |
|
|
\[
{}t y^{\prime }+y = t^{3}
\] |
[_linear] |
✓ |
1.938 |
|
|
\[
{}t^{3} y^{\prime }+t^{4} y = 2 t^{3}
\] |
[_linear] |
✓ |
1.509 |
|
|
\[
{}2 y^{\prime }+t y = \ln \left (t \right )
\] |
[_linear] |
✓ |
1.839 |
|
|
\[
{}y^{\prime }+y \sec \left (t \right ) = t
\] |
[_linear] |
✓ |
2.156 |
|
|
\[
{}y^{\prime }+\frac {y}{t -3} = \frac {1}{t -1}
\] |
[_linear] |
✓ |
1.672 |
|
|
\[
{}\left (t -2\right ) y^{\prime }+\left (t^{2}-4\right ) y = \frac {1}{t +2}
\] |
[_linear] |
✓ |
1.903 |
|
|
\[
{}y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}} = t
\] |
[_linear] |
✓ |
2.132 |
|
|
\[
{}y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}} = t
\] |
[_linear] |
✓ |
2.706 |
|
|
\[
{}t y^{\prime }+y = t \sin \left (t \right )
\] |
[_linear] |
✓ |
1.615 |
|
|
\[
{}y^{\prime }+y \tan \left (t \right ) = \sin \left (t \right )
\] |
[_linear] |
✓ |
2.179 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.527 |
|
|
\[
{}y^{\prime } = t y^{2}
\] |
[_separable] |
✓ |
2.579 |
|
|
\[
{}y^{\prime } = -\frac {t}{y}
\] |
[_separable] |
✓ |
6.137 |
|
|
\[
{}y^{\prime } = -y^{3}
\] |
[_quadrature] |
✓ |
1.977 |
|
|
\[
{}y^{\prime } = \frac {x}{y^{2}}
\] |
[_separable] |
✓ |
2.362 |
|
|
\[
{}\frac {1}{2 \sqrt {t}}+y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.268 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x^{2}}
\] |
[_separable] |
✓ |
3.242 |
|
|
\[
{}y^{\prime } = \frac {1+y^{2}}{y}
\] |
[_quadrature] |
✓ |
4.554 |
|
|
\[
{}6+4 t^{3}+\left (5+\frac {9}{y^{8}}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.859 |
|
|
\[
{}\frac {6}{t^{9}}-\frac {6}{t^{3}}+t^{7}+\left (9+\frac {1}{s^{2}}-4 s^{8}\right ) s^{\prime } = 0
\] |
[_separable] |
✓ |
2.056 |
|
|
\[
{}4 \sinh \left (4 y\right ) y^{\prime } = 6 \cosh \left (3 x \right )
\] |
[_separable] |
✓ |
2.762 |
|