|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.143 |
|
|
\[
{}t^{2} y^{\prime \prime }-12 t y^{\prime }+42 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.048 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.047 |
|
|
\[
{}y^{\prime } = 4 x^{3}-x +2
\] |
[_quadrature] |
✓ |
0.450 |
|
|
\[
{}y^{\prime } = \sin \left (2 t \right )-\cos \left (2 t \right )
\] |
[_quadrature] |
✓ |
0.693 |
|
|
\[
{}y^{\prime } = \frac {\cos \left (\frac {1}{x}\right )}{x^{2}}
\] |
[_quadrature] |
✓ |
0.765 |
|
|
\[
{}y^{\prime } = \frac {\ln \left (x \right )}{x}
\] |
[_quadrature] |
✓ |
0.510 |
|
|
\[
{}y^{\prime } = \frac {\left (x -4\right ) y^{3}}{x^{3} \left (y-2\right )}
\] |
[_separable] |
✓ |
2.983 |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 x y}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.175 |
|
|
\[
{}x y^{\prime }+y = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.132 |
|
|
\[
{}16 y^{\prime \prime }+24 y^{\prime }+153 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.837 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 y \\ y^{\prime }=-x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.615 |
|
|
\[
{}4 x \left (y^{2}+x^{2}\right )-5 y+4 y \left (x^{2}+y^{2}-5 x \right ) y^{\prime } = 0
\] |
[_rational] |
✗ |
32.165 |
|
|
\[
{}y^{\prime } = \sin \left (x \right )^{4}
\] |
[_quadrature] |
✓ |
0.759 |
|
|
\[
{}y^{\prime \prime \prime \prime }+\frac {25 y^{\prime \prime }}{2}-5 y^{\prime }+\frac {629 y}{16} = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.103 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 y \\ y^{\prime }=-4 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.426 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x+4 y \\ y^{\prime }=2 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.519 |
|
|
\[
{}y^{\prime }+\cos \left (x \right ) y = 0
\] |
[_separable] |
✓ |
1.388 |
|
|
\[
{}y^{\prime }-y = \sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.193 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.818 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+45 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.854 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }-16 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.331 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.978 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
8.017 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.987 |
|
|
\[
{}2 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.340 |
|
|
\[
{}y \cos \left (x y\right )+\sin \left (x \right )+x \cos \left (x y\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
35.278 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{-x^{2}}
\] |
[_quadrature] |
✓ |
0.329 |
|
|
\[
{}y^{\prime } = x^{2} \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.354 |
|
|
\[
{}y^{\prime } = \frac {2 x^{2}-x +1}{\left (x -1\right ) \left (x^{2}+1\right )}
\] |
[_quadrature] |
✓ |
0.376 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{\sqrt {x^{2}-1}}
\] |
[_quadrature] |
✓ |
0.385 |
|
|
\[
{}y^{\prime }+2 y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.342 |
|
|
\[
{}y^{\prime \prime }+4 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.220 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.700 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )^{2} \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.571 |
|
|
\[
{}y^{\prime } = \frac {4 x -9}{3 \left (x -3\right )^{{2}/{3}}}
\] |
[_quadrature] |
✓ |
0.540 |
|
|
\[
{}y^{\prime }+t^{2} = y^{2}
\] |
[_Riccati] |
✓ |
1.428 |
|
|
\[
{}y^{\prime }+t^{2} = \frac {1}{y^{2}}
\] |
[_rational] |
✗ |
0.677 |
|
|
\[
{}y^{\prime } = y+\frac {1}{-t +1}
\] |
[_linear] |
✓ |
1.157 |
|
|
\[
{}y^{\prime } = y^{{1}/{5}}
\] |
[_quadrature] |
✓ |
1.717 |
|
|
\[
{}\frac {y^{\prime }}{t} = \sqrt {y}
\] |
[_separable] |
✓ |
4.530 |
|
|
\[
{}y^{\prime } = 4 t^{2}-t y^{2}
\] |
[_Riccati] |
✓ |
2.454 |
|
|
\[
{}y^{\prime } = y \sqrt {t}
\] |
[_separable] |
✓ |
1.754 |
|
|
\[
{}y^{\prime } = 6 y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
1.629 |
|
|
\[
{}t y^{\prime } = y
\] |
[_separable] |
✓ |
1.228 |
|
|
\[
{}y^{\prime } = y \tan \left (t \right )
\] |
[_separable] |
✓ |
1.870 |
|
|
\[
{}y^{\prime } = \frac {1}{t^{2}+1}
\] |
[_quadrature] |
✓ |
0.506 |
|
|
\[
{}y^{\prime } = \sqrt {y^{2}-1}
\] |
[_quadrature] |
✓ |
10.656 |
|
|
\[
{}y^{\prime } = \sqrt {y^{2}-1}
\] |
[_quadrature] |
✓ |
7.452 |
|
|
\[
{}y^{\prime } = \sqrt {y^{2}-1}
\] |
[_quadrature] |
✓ |
11.417 |
|
|
\[
{}y^{\prime } = \sqrt {y^{2}-1}
\] |
[_quadrature] |
✓ |
4.985 |
|
|
\[
{}y^{\prime } = \sqrt {25-y^{2}}
\] |
[_quadrature] |
✓ |
222.026 |
|
|
\[
{}y^{\prime } = \sqrt {25-y^{2}}
\] |
[_quadrature] |
✓ |
3.243 |
|
|
\[
{}y^{\prime } = \sqrt {25-y^{2}}
\] |
[_quadrature] |
✓ |
8.827 |
|
|
\[
{}y^{\prime } = \sqrt {25-y^{2}}
\] |
[_quadrature] |
✓ |
74.030 |
|
|
\[
{}t y^{\prime }+y = t^{3}
\] |
[_linear] |
✓ |
1.691 |
|
|
\[
{}t^{3} y^{\prime }+t^{4} y = 2 t^{3}
\] |
[_linear] |
✓ |
1.330 |
|
|
\[
{}2 y^{\prime }+t y = \ln \left (t \right )
\] |
[_linear] |
✓ |
1.806 |
|
|
\[
{}y^{\prime }+y \sec \left (t \right ) = t
\] |
[_linear] |
✓ |
2.058 |
|
|
\[
{}y^{\prime }+\frac {y}{t -3} = \frac {1}{t -1}
\] |
[_linear] |
✓ |
1.534 |
|
|
\[
{}\left (t -2\right ) y^{\prime }+\left (t^{2}-4\right ) y = \frac {1}{t +2}
\] |
[_linear] |
✓ |
1.829 |
|
|
\[
{}y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}} = t
\] |
[_linear] |
✓ |
2.497 |
|
|
\[
{}y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}} = t
\] |
[_linear] |
✓ |
2.988 |
|
|
\[
{}t y^{\prime }+y = t \sin \left (t \right )
\] |
[_linear] |
✓ |
1.495 |
|
|
\[
{}y^{\prime }+y \tan \left (t \right ) = \sin \left (t \right )
\] |
[_linear] |
✓ |
2.268 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.202 |
|
|
\[
{}y^{\prime } = t y^{2}
\] |
[_separable] |
✓ |
2.255 |
|
|
\[
{}y^{\prime } = -\frac {t}{y}
\] |
[_separable] |
✓ |
5.856 |
|
|
\[
{}y^{\prime } = -y^{3}
\] |
[_quadrature] |
✓ |
1.707 |
|
|
\[
{}y^{\prime } = \frac {x}{y^{2}}
\] |
[_separable] |
✓ |
2.174 |
|
|
\[
{}\frac {1}{2 \sqrt {t}}+y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.252 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x^{2}}
\] |
[_separable] |
✓ |
3.137 |
|
|
\[
{}y^{\prime } = \frac {1+y^{2}}{y}
\] |
[_quadrature] |
✓ |
4.319 |
|
|
\[
{}6+4 t^{3}+\left (5+\frac {9}{y^{8}}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.773 |
|
|
\[
{}\frac {6}{t^{9}}-\frac {6}{t^{3}}+t^{7}+\left (9+\frac {1}{s^{2}}-4 s^{8}\right ) s^{\prime } = 0
\] |
[_separable] |
✓ |
2.132 |
|
|
\[
{}4 \sinh \left (4 y\right ) y^{\prime } = 6 \cosh \left (3 x \right )
\] |
[_separable] |
✓ |
2.750 |
|
|
\[
{}y^{\prime } = \frac {y+1}{t +1}
\] |
[_separable] |
✓ |
1.446 |
|
|
\[
{}y^{\prime } = \frac {y+2}{2 t +1}
\] |
[_separable] |
✓ |
1.464 |
|
|
\[
{}\frac {3}{t^{2}} = \left (\frac {1}{\sqrt {y}}+\sqrt {y}\right ) y^{\prime }
\] |
[_separable] |
✓ |
1.825 |
|
|
\[
{}3 \sin \left (x \right )-4 \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.825 |
|
|
\[
{}\cos \left (y\right ) y^{\prime } = 8 \sin \left (8 t \right )
\] |
[_separable] |
✓ |
3.116 |
|
|
\[
{}y^{\prime }+k y = 0
\] |
[_quadrature] |
✓ |
0.714 |
|
|
\[
{}\left (5 x^{5}-4 \cos \left (x\right )\right ) x^{\prime }+2 \cos \left (9 t \right )+2 \sin \left (7 t \right ) = 0
\] |
[_separable] |
✓ |
40.592 |
|
|
\[
{}\cosh \left (6 t \right )+5 \sinh \left (4 t \right )+20 \sinh \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
5.777 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 y+10 t}
\] |
[_separable] |
✓ |
1.987 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3 y+2 t}
\] |
[_separable] |
✓ |
2.059 |
|
|
\[
{}\sin \left (t \right )^{2} = \cos \left (y\right )^{2} y^{\prime }
\] |
[_separable] |
✓ |
2.451 |
|
|
\[
{}3 \sin \left (t \right )-\sin \left (3 t \right ) = \left (\cos \left (4 y\right )-4 \cos \left (y\right )\right ) y^{\prime }
\] |
[_separable] |
✓ |
35.997 |
|
|
\[
{}x^{\prime } = \frac {\sec \left (t \right )^{2}}{\sec \left (x\right ) \tan \left (x\right )}
\] |
[_separable] |
✓ |
36.487 |
|
|
\[
{}\left (2-\frac {5}{y^{2}}\right ) y^{\prime }+4 \cos \left (x \right )^{2} = 0
\] |
[_separable] |
✓ |
2.127 |
|
|
\[
{}y^{\prime } = \frac {t^{3}}{y \sqrt {\left (1-y^{2}\right ) \left (t^{4}+9\right )}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.641 |
|
|
\[
{}\tan \left (y\right ) \sec \left (y\right )^{2} y^{\prime }+\cos \left (2 x \right )^{3} \sin \left (2 x \right ) = 0
\] |
[_separable] |
✓ |
39.833 |
|
|
\[
{}y^{\prime } = \frac {\left (1+2 \,{\mathrm e}^{y}\right ) {\mathrm e}^{-y}}{t \ln \left (t \right )}
\] |
[_separable] |
✓ |
1.827 |
|
|
\[
{}x \sin \left (x^{2}\right ) = \frac {\cos \left (\sqrt {y}\right ) y^{\prime }}{\sqrt {y}}
\] |
[_separable] |
✓ |
5.889 |
|
|
\[
{}\frac {-2+x}{x^{2}-4 x +3} = \frac {\left (1-\frac {1}{y}\right )^{2} y^{\prime }}{y^{2}}
\] |
[_separable] |
✓ |
2.047 |
|
|
\[
{}\frac {\cos \left (y\right ) y^{\prime }}{\left (1-\sin \left (y\right )\right )^{2}} = \sin \left (x \right )^{3} \cos \left (x \right )
\] |
[_separable] |
✓ |
43.932 |
|
|
\[
{}y^{\prime } = \frac {\left (5-2 \cos \left (x \right )\right )^{3} \sin \left (x \right ) \cos \left (y\right )^{4}}{\sin \left (y\right )}
\] |
[_separable] |
✓ |
42.722 |
|
|
\[
{}\frac {\sqrt {\ln \left (x \right )}}{x} = \frac {{\mathrm e}^{\frac {3}{y}} y^{\prime }}{y}
\] |
[_separable] |
✓ |
1.585 |
|
|
\[
{}y^{\prime } = \frac {5^{-t}}{y^{2}}
\] |
[_separable] |
✓ |
2.136 |
|
|
\[
{}y^{\prime } = t^{2} y^{2}+y^{2}-t^{2}-1
\] |
[_separable] |
✓ |
2.198 |
|