|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime \prime \prime }+\frac {25 y^{\prime \prime }}{2}-5 y^{\prime }+\frac {629 y}{16} = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.094 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 y \\ y^{\prime }=-4 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.393 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x+4 y \\ y^{\prime }=2 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.480 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
1.198 |
|
|
\[
{}y^{\prime }-y = \sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.058 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.728 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+45 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.430 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x -16 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.090 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.661 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
6.904 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.859 |
|
|
\[
{}2 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.190 |
|
|
\[
{}y \cos \left (y x \right )+\sin \left (x \right )+x \cos \left (y x \right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
69.091 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{-x^{2}}
\] |
[_quadrature] |
✓ |
0.273 |
|
|
\[
{}y^{\prime } = x^{2} \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.304 |
|
|
\[
{}y^{\prime } = \frac {2 x^{2}-x +1}{\left (x -1\right ) \left (x^{2}+1\right )}
\] |
[_quadrature] |
✓ |
0.318 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{\sqrt {x^{2}-1}}
\] |
[_quadrature] |
✓ |
0.329 |
|
|
\[
{}y^{\prime }+2 y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.132 |
|
|
\[
{}y^{\prime \prime }+4 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.664 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.356 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )^{2} \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.511 |
|
|
\[
{}y^{\prime } = \frac {4 x -9}{3 \left (x -3\right )^{{2}/{3}}}
\] |
[_quadrature] |
✓ |
0.428 |
|
|
\[
{}y^{\prime }+t^{2} = y^{2}
\] |
[_Riccati] |
✓ |
1.223 |
|
|
\[
{}y^{\prime }+t^{2} = \frac {1}{y^{2}}
\] |
[_rational] |
✗ |
0.377 |
|
|
\[
{}y^{\prime } = y+\frac {1}{1-t}
\] |
[_linear] |
✓ |
1.062 |
|
|
\[
{}y^{\prime } = y^{{1}/{5}}
\] |
[_quadrature] |
✓ |
0.695 |
|
|
\[
{}\frac {y^{\prime }}{t} = \sqrt {y}
\] |
[_separable] |
✓ |
2.056 |
|
|
\[
{}y^{\prime } = 4 t^{2}-t y^{2}
\] |
[_Riccati] |
✓ |
2.390 |
|
|
\[
{}y^{\prime } = y \sqrt {t}
\] |
[_separable] |
✓ |
1.469 |
|
|
\[
{}y^{\prime } = 6 y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
0.681 |
|
|
\[
{}t y^{\prime } = y
\] |
[_separable] |
✓ |
1.086 |
|
|
\[
{}y^{\prime } = y \tan \left (t \right )
\] |
[_separable] |
✓ |
1.592 |
|
|
\[
{}y^{\prime } = \frac {1}{t^{2}+1}
\] |
[_quadrature] |
✓ |
0.424 |
|
|
\[
{}y^{\prime } = \sqrt {-1+y^{2}}
\] |
[_quadrature] |
✓ |
2.807 |
|
|
\[
{}y^{\prime } = \sqrt {-1+y^{2}}
\] |
[_quadrature] |
✓ |
5.603 |
|
|
\[
{}y^{\prime } = \sqrt {-1+y^{2}}
\] |
[_quadrature] |
✓ |
2.934 |
|
|
\[
{}y^{\prime } = \sqrt {-1+y^{2}}
\] |
[_quadrature] |
✓ |
3.172 |
|
|
\[
{}y^{\prime } = \sqrt {25-y^{2}}
\] |
[_quadrature] |
✓ |
2.264 |
|
|
\[
{}y^{\prime } = \sqrt {25-y^{2}}
\] |
[_quadrature] |
✓ |
2.228 |
|
|
\[
{}y^{\prime } = \sqrt {25-y^{2}}
\] |
[_quadrature] |
✓ |
2.047 |
|
|
\[
{}y^{\prime } = \sqrt {25-y^{2}}
\] |
[_quadrature] |
✓ |
6.855 |
|
|
\[
{}t y^{\prime }+y = t^{3}
\] |
[_linear] |
✓ |
1.393 |
|
|
\[
{}t^{3} y^{\prime }+t^{4} y = 2 t^{3}
\] |
[_linear] |
✓ |
1.198 |
|
|
\[
{}2 y^{\prime }+t y = \ln \left (t \right )
\] |
[_linear] |
✓ |
1.627 |
|
|
\[
{}y^{\prime }+y \sec \left (t \right ) = t
\] |
[_linear] |
✓ |
1.782 |
|
|
\[
{}y^{\prime }+\frac {y}{t -3} = \frac {1}{t -1}
\] |
[_linear] |
✓ |
1.456 |
|
|
\[
{}\left (t -2\right ) y^{\prime }+\left (t^{2}-4\right ) y = \frac {1}{t +2}
\] |
[_linear] |
✓ |
1.711 |
|
|
\[
{}y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}} = t
\] |
[_linear] |
✓ |
2.391 |
|
|
\[
{}y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}} = t
\] |
[_linear] |
✓ |
3.016 |
|
|
\[
{}t y^{\prime }+y = t \sin \left (t \right )
\] |
[_linear] |
✓ |
1.352 |
|
|
\[
{}y^{\prime }+y \tan \left (t \right ) = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.955 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
0.486 |
|
|
\[
{}y^{\prime } = t y^{2}
\] |
[_separable] |
✓ |
1.901 |
|
|
\[
{}y^{\prime } = -\frac {t}{y}
\] |
[_separable] |
✓ |
5.189 |
|
|
\[
{}y^{\prime } = -y^{3}
\] |
[_quadrature] |
✓ |
0.611 |
|
|
\[
{}y^{\prime } = \frac {x}{y^{2}}
\] |
[_separable] |
✓ |
1.932 |
|
|
\[
{}\frac {1}{2 \sqrt {t}}+y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.047 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x^{2}}
\] |
[_separable] |
✓ |
1.892 |
|
|
\[
{}y^{\prime } = \frac {1+y^{2}}{y}
\] |
[_quadrature] |
✓ |
0.760 |
|
|
\[
{}6+4 t^{3}+\left (5+\frac {9}{y^{8}}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.720 |
|
|
\[
{}\frac {6}{t^{9}}-\frac {6}{t^{3}}+t^{7}+\left (9+\frac {1}{s^{2}}-4 s^{8}\right ) s^{\prime } = 0
\] |
[_separable] |
✓ |
2.051 |
|
|
\[
{}4 \sinh \left (4 y\right ) y^{\prime } = 6 \cosh \left (3 x \right )
\] |
[_separable] |
✓ |
3.418 |
|
|
\[
{}y^{\prime } = \frac {y+1}{1+t}
\] |
[_separable] |
✓ |
1.330 |
|
|
\[
{}y^{\prime } = \frac {y+2}{2 t +1}
\] |
[_separable] |
✓ |
1.365 |
|
|
\[
{}\frac {3}{t^{2}} = \left (\frac {1}{\sqrt {y}}+\sqrt {y}\right ) y^{\prime }
\] |
[_separable] |
✓ |
1.686 |
|
|
\[
{}3 \sin \left (x \right )-4 \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.943 |
|
|
\[
{}\cos \left (y\right ) y^{\prime } = 8 \sin \left (8 t \right )
\] |
[_separable] |
✓ |
4.318 |
|
|
\[
{}y^{\prime }+k y = 0
\] |
[_quadrature] |
✓ |
0.413 |
|
|
\[
{}\left (5 x^{5}-4 \cos \left (x\right )\right ) x^{\prime }+2 \cos \left (9 t \right )+2 \sin \left (7 t \right ) = 0
\] |
[_separable] |
✓ |
74.166 |
|
|
\[
{}\cosh \left (6 t \right )+5 \sinh \left (4 t \right )+20 \sinh \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
8.457 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 y+10 t}
\] |
[_separable] |
✓ |
1.624 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3 y+2 t}
\] |
[_separable] |
✓ |
1.642 |
|
|
\[
{}\sin \left (t \right )^{2} = \cos \left (y\right )^{2} y^{\prime }
\] |
[_separable] |
✓ |
2.465 |
|
|
\[
{}3 \sin \left (t \right )-\sin \left (3 t \right ) = \left (\cos \left (4 y\right )-4 \cos \left (y\right )\right ) y^{\prime }
\] |
[_separable] |
✓ |
71.112 |
|
|
\[
{}x^{\prime } = \frac {\sec \left (t \right )^{2}}{\sec \left (x\right ) \tan \left (x\right )}
\] |
[_separable] |
✓ |
86.381 |
|
|
\[
{}\left (2-\frac {5}{y^{2}}\right ) y^{\prime }+4 \cos \left (x \right )^{2} = 0
\] |
[_separable] |
✓ |
2.078 |
|
|
\[
{}y^{\prime } = \frac {t^{3}}{y \sqrt {\left (1-y^{2}\right ) \left (t^{4}+9\right )}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.506 |
|
|
\[
{}\tan \left (y\right ) \sec \left (y\right )^{2} y^{\prime }+\cos \left (2 x \right )^{3} \sin \left (2 x \right ) = 0
\] |
[_separable] |
✓ |
72.079 |
|
|
\[
{}y^{\prime } = \frac {\left (1+2 \,{\mathrm e}^{y}\right ) {\mathrm e}^{-y}}{t \ln \left (t \right )}
\] |
[_separable] |
✓ |
1.786 |
|
|
\[
{}x \sin \left (x^{2}\right ) = \frac {\cos \left (\sqrt {y}\right ) y^{\prime }}{\sqrt {y}}
\] |
[_separable] |
✓ |
5.416 |
|
|
\[
{}\frac {x -2}{x^{2}-4 x +3} = \frac {\left (1-\frac {1}{y}\right )^{2} y^{\prime }}{y^{2}}
\] |
[_separable] |
✓ |
1.904 |
|
|
\[
{}\frac {\cos \left (y\right ) y^{\prime }}{\left (1-\sin \left (y\right )\right )^{2}} = \sin \left (x \right )^{3} \cos \left (x \right )
\] |
[_separable] |
✓ |
76.257 |
|
|
\[
{}y^{\prime } = \frac {\left (5-2 \cos \left (x \right )\right )^{3} \sin \left (x \right ) \cos \left (y\right )^{4}}{\sin \left (y\right )}
\] |
[_separable] |
✓ |
81.386 |
|
|
\[
{}\frac {\sqrt {\ln \left (x \right )}}{x} = \frac {{\mathrm e}^{\frac {3}{y}} y^{\prime }}{y}
\] |
[_separable] |
✓ |
1.456 |
|
|
\[
{}y^{\prime } = \frac {5^{-t}}{y^{2}}
\] |
[_separable] |
✓ |
1.806 |
|
|
\[
{}y^{\prime } = t^{2} y^{2}+y^{2}-t^{2}-1
\] |
[_separable] |
✓ |
1.909 |
|
|
\[
{}y^{\prime } = y^{2}-3 y+2
\] |
[_quadrature] |
✓ |
0.514 |
|
|
\[
{}4 \left (x -1\right )^{2} y^{\prime }-3 \left (3+y\right )^{2} = 0
\] |
[_separable] |
✓ |
1.768 |
|
|
\[
{}y^{\prime } = \sin \left (t -y\right )+\sin \left (y+t \right )
\] |
[_separable] |
✓ |
5.074 |
|
|
\[
{}y^{\prime } = y^{3}+1
\] |
[_quadrature] |
✓ |
1.242 |
|
|
\[
{}y^{\prime } = y^{3}-1
\] |
[_quadrature] |
✓ |
1.716 |
|
|
\[
{}y^{\prime } = y^{3}+y
\] |
[_quadrature] |
✓ |
2.485 |
|
|
\[
{}y^{\prime } = y^{3}-y^{2}
\] |
[_quadrature] |
✓ |
0.645 |
|
|
\[
{}y^{\prime } = y^{3}-y
\] |
[_quadrature] |
✓ |
1.040 |
|
|
\[
{}y^{\prime } = y^{3}+y
\] |
[_quadrature] |
✓ |
2.513 |
|
|
\[
{}y^{\prime } = x^{3}
\] |
[_quadrature] |
✓ |
0.329 |
|
|
\[
{}y^{\prime } = \cos \left (t \right )
\] |
[_quadrature] |
✓ |
0.416 |
|
|
\[
{}1 = \cos \left (y\right ) y^{\prime }
\] |
[_quadrature] |
✓ |
0.590 |
|
|
\[
{}\sin \left (y \right )^{2} = x^{\prime }
\] |
[_quadrature] |
✓ |
0.523 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {t}}{y}
\] |
[_separable] |
✓ |
7.241 |
|