|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\frac {2 t y}{t^{2}+1}+y^{\prime } = \frac {1}{t^{2}+1}
\] |
[_linear] |
✓ |
1.215 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{t} t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.306 |
|
|
\[
{}t^{2} y+y^{\prime } = 1
\] |
[_linear] |
✓ |
1.294 |
|
|
\[
{}t^{2} y+y^{\prime } = t^{2}
\] |
[_separable] |
✓ |
1.515 |
|
|
\[
{}\frac {t y}{t^{2}+1}+y^{\prime } = 1-\frac {t^{3} y}{t^{4}+1}
\] |
[_linear] |
✓ |
1.984 |
|
|
\[
{}\sqrt {t^{2}+1}\, y+y^{\prime } = 0
\] |
[_separable] |
✓ |
3.931 |
|
|
\[
{}\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime } = 0
\] |
[_separable] |
✓ |
1.898 |
|
|
\[
{}y^{\prime }-2 t y = t
\] |
[_separable] |
✓ |
1.951 |
|
|
\[
{}t y+y^{\prime } = t +1
\] |
[_linear] |
✓ |
1.625 |
|
|
\[
{}y^{\prime }+y = \frac {1}{t^{2}+1}
\] |
[_linear] |
✓ |
1.866 |
|
|
\[
{}y^{\prime }-2 t y = 1
\] |
[_linear] |
✓ |
1.382 |
|
|
\[
{}t y+\left (t^{2}+1\right ) y^{\prime } = \left (t^{2}+1\right )^{{5}/{2}}
\] |
[_linear] |
✓ |
2.036 |
|
|
\[
{}4 t y+\left (t^{2}+1\right ) y^{\prime } = t
\] |
[_separable] |
✓ |
2.099 |
|
|
\[
{}y^{\prime }+\frac {y}{t} = \frac {1}{t^{2}}
\] |
[_linear] |
✓ |
0.214 |
|
|
\[
{}y^{\prime }+\frac {y}{\sqrt {t}} = {\mathrm e}^{\frac {\sqrt {t}}{2}}
\] |
[_linear] |
✓ |
0.282 |
|
|
\[
{}y^{\prime }+\frac {y}{t} = \cos \left (t \right )+\frac {\sin \left (t \right )}{t}
\] |
[_linear] |
✓ |
0.288 |
|
|
\[
{}y^{\prime }+\tan \left (t \right ) y = \cos \left (t \right ) \sin \left (t \right )
\] |
[_linear] |
✓ |
0.317 |
|
|
\[
{}\left (t^{2}+1\right ) y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
2.267 |
|
|
\[
{}y^{\prime } = \left (t +1\right ) \left (y+1\right )
\] |
[_separable] |
✓ |
1.557 |
|
|
\[
{}y^{\prime } = 1-t +y^{2}-t y^{2}
\] |
[_separable] |
✓ |
2.273 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3+t +y}
\] |
[_separable] |
✓ |
2.689 |
|
|
\[
{}\cos \left (y\right ) \sin \left (t \right ) y^{\prime } = \cos \left (t \right ) \sin \left (y\right )
\] |
[_separable] |
✓ |
2.859 |
|
|
\[
{}t^{2} \left (1+y^{2}\right )+2 y y^{\prime } = 0
\] |
[_separable] |
✓ |
3.007 |
|
|
\[
{}y^{\prime } = \frac {2 t}{y+t^{2} y}
\] |
[_separable] |
✓ |
2.316 |
|
|
\[
{}\sqrt {t^{2}+1}\, y^{\prime } = \frac {t y^{3}}{\sqrt {t^{2}+1}}
\] |
[_separable] |
✓ |
4.348 |
|
|
\[
{}y^{\prime } = \frac {3 t^{2}+4 t +2}{-2+2 y}
\] |
[_separable] |
✓ |
2.467 |
|
|
\[
{}\cos \left (y\right ) y^{\prime } = -\frac {t \sin \left (y\right )}{t^{2}+1}
\] |
[_separable] |
✓ |
3.152 |
|
|
\[
{}y^{\prime } = k \left (a -y\right ) \left (b -y\right )
\] |
[_quadrature] |
✓ |
33.839 |
|
|
\[
{}3 t y^{\prime } = \cos \left (t \right ) y
\] |
[_separable] |
✓ |
3.052 |
|
|
\[
{}t y^{\prime } = y+\sqrt {t^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.227 |
|
|
\[
{}2 t y y^{\prime } = 3 y^{2}-t^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
137.026 |
|
|
\[
{}\left (t -\sqrt {t y}\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
11.855 |
|
|
\[
{}y^{\prime } = \frac {y+t}{-y+t}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
39.214 |
|
|
\[
{}{\mathrm e}^{\frac {t}{y}} \left (-t +y\right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.119 |
|
|
\[
{}y^{\prime } = \frac {t +y+1}{t -y+3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
37.126 |
|
|
\[
{}1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.318 |
|
|
\[
{}t +2 y+3+\left (2 t +4 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.999 |
|
|
\[
{}2 t \sin \left (y\right )+{\mathrm e}^{t} y^{3}+\left (t^{2} \cos \left (y\right )+3 \,{\mathrm e}^{t} y^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
3.865 |
|
|
\[
{}1+{\mathrm e}^{t y} \left (1+t y\right )+\left (1+{\mathrm e}^{t y} t^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
1.944 |
|
|
\[
{}\sec \left (t \right ) \tan \left (t \right )+\sec \left (t \right )^{2} y+\left (\tan \left (t \right )+2 y\right ) y^{\prime } = 0
\] |
[_exact, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
12.903 |
|
|
\[
{}\frac {y^{2}}{2}-2 \,{\mathrm e}^{t} y+\left (-{\mathrm e}^{t}+y\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.661 |
|
|
\[
{}2 t y^{3}+3 t^{2} y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.785 |
|
|
\[
{}2 t \cos \left (y\right )+3 t^{2} y+\left (t^{3}-t^{2} \sin \left (y\right )-y\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.729 |
|
|
\[
{}3 t^{2}+4 t y+\left (2 t^{2}+2 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.773 |
|
|
\[
{}2 t -2 \,{\mathrm e}^{t y} \sin \left (2 t \right )+{\mathrm e}^{t y} \cos \left (2 t \right ) y+\left (-3+{\mathrm e}^{t y} t \cos \left (2 t \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
38.121 |
|
|
\[
{}3 t y+y^{2}+\left (t^{2}+t y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
386.477 |
|
|
\[
{}y^{\prime } = y^{2}+\cos \left (t^{2}\right )
\] |
[_Riccati] |
✗ |
3.780 |
|
|
\[
{}y^{\prime } = 1+y+y^{2} \cos \left (t \right )
\] |
[_Riccati] |
✗ |
17.134 |
|
|
\[
{}y^{\prime } = t +y^{2}
\] |
[[_Riccati, _special]] |
✓ |
14.909 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\] |
[_Riccati] |
✗ |
1.622 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\] |
[_Riccati] |
✗ |
1.611 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\] |
[_Riccati] |
✗ |
1.613 |
|
|
\[
{}y^{\prime } = y+{\mathrm e}^{-y}+{\mathrm e}^{-t}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.542 |
|
|
\[
{}y^{\prime } = y^{3}+{\mathrm e}^{-5 t}
\] |
[_Abel] |
✗ |
1.014 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{\left (-t +y\right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
3.207 |
|
|
\[
{}y^{\prime } = \left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.759 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-t}+\ln \left (1+y^{2}\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
2.056 |
|
|
\[
{}y^{\prime } = \frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800}
\] |
[_Bernoulli] |
✓ |
5.809 |
|
|
\[
{}y^{\prime } = t^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.912 |
|
|
\[
{}y^{\prime } = t \left (y+1\right )
\] |
[_separable] |
✓ |
1.672 |
|
|
\[
{}y^{\prime } = t \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
6.377 |
|
|
\[
{}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.480 |
|
|
\[
{}y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.110 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.022 |
|
|
\[
{}6 y^{\prime \prime }-7 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.851 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.108 |
|
|
\[
{}3 y^{\prime \prime }+6 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.954 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.398 |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime }-10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.462 |
|
|
\[
{}5 y^{\prime \prime }+5 y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.633 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.556 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.895 |
|
|
\[
{}t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.704 |
|
|
\[
{}t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.869 |
|
|
\[
{}t^{2} y^{\prime \prime }-t y^{\prime }-2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.081 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.924 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.098 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.034 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.972 |
|
|
\[
{}4 y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.094 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.092 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.670 |
|
|
\[
{}2 y^{\prime \prime }-y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.979 |
|
|
\[
{}3 y^{\prime \prime }-2 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.487 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.067 |
|
|
\[
{}t^{2} y^{\prime \prime }+2 t y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.648 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.951 |
|
|
\[
{}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.963 |
|
|
\[
{}9 y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.368 |
|
|
\[
{}4 y^{\prime \prime }-4 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.348 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.332 |
|
|
\[
{}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.405 |
|
|
\[
{}y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.263 |
|
|
\[
{}y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.523 |
|
|
\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\] |
[_Gegenbauer] |
✓ |
1.454 |
|
|
\[
{}\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.031 |
|
|
\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y = 0
\] |
[_Gegenbauer] |
✓ |
1.182 |
|
|
\[
{}\left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.128 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.504 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.064 |
|