|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime }-\frac {y}{2} = 5 \cos \left (t \right )+2 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
2.040 |
|
|
\[
{}y^{\prime }+4 y = 8 \cos \left (4 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.615 |
|
|
\[
{}y^{\prime }+10 y = 2 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.314 |
|
|
\[
{}y^{\prime }-3 y = 27 t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.306 |
|
|
\[
{}y^{\prime }-y = 2 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.240 |
|
|
\[
{}y^{\prime }+y = 4+3 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.363 |
|
|
\[
{}y^{\prime }+y = 2 \cos \left (t \right )+t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.677 |
|
|
\[
{}y^{\prime }+\frac {y}{2} = \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.638 |
|
|
\[
{}y^{\prime }-\frac {y}{2} = \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.625 |
|
|
\[
{}y^{\prime } t +y = t \cos \left (t \right )
\] |
[_linear] |
✓ |
1.395 |
|
|
\[
{}y^{\prime }+y = t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.469 |
|
|
\[
{}y^{\prime }+y = \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.697 |
|
|
\[
{}y^{\prime }+y = \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.689 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.562 |
|
|
\[
{}y^{2}-\frac {y}{2 \sqrt {t}}+\left (2 t y-\sqrt {t}+1\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
50.287 |
|
|
\[
{}\frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}} = 0
\] |
[_separable] |
✓ |
3.707 |
|
|
\[
{}y \cos \left (t y\right )+t \cos \left (t y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.500 |
|
|
\[
{}y \sec \left (t \right )^{2}+2 t +\tan \left (t \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
10.472 |
|
|
\[
{}3 t y^{2}+y^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.718 |
|
|
\[
{}t -\sin \left (t \right ) y+\left (y^{6}+\cos \left (t \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.957 |
|
|
\[
{}y \sin \left (2 t \right )+\left (\sqrt {y}+\cos \left (2 t \right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
5.701 |
|
|
\[
{}\ln \left (t y\right )+\frac {t y^{\prime }}{y} = 0
\] |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
1.733 |
|
|
\[
{}{\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y} = 0
\] |
[_separable] |
✓ |
2.444 |
|
|
\[
{}3 t^{2}-y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.492 |
|
|
\[
{}-1+3 y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
7.372 |
|
|
\[
{}y^{2}+2 t y y^{\prime } = 0
\] |
[_separable] |
✓ |
2.489 |
|
|
\[
{}\frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}} = 0
\] |
[_separable] |
✓ |
2.444 |
|
|
\[
{}2 t +y^{3}+\left (3 t y^{2}+4\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.331 |
|
|
\[
{}-\frac {1}{y}+\left (\frac {t}{y^{2}}+3 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
2.984 |
|
|
\[
{}2 t y+\left (t^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
4.117 |
|
|
\[
{}2 t y^{3}+\left (1+3 t^{2} y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
1.829 |
|
|
\[
{}\sin \left (y\right )^{2}+t \sin \left (2 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
5.224 |
|
|
\[
{}3 t^{2}+3 y^{2}+6 t y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
4.971 |
|
|
\[
{}{\mathrm e}^{t} \sin \left (y\right )+\left (1+{\mathrm e}^{t} \cos \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.161 |
|
|
\[
{}3 t^{2} y+3 y^{2}-1+\left (t^{3}+6 t y\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.588 |
|
|
\[
{}-2 t y^{2} \sin \left (t^{2}\right )+2 y \cos \left (t^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.576 |
|
|
\[
{}2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
38.916 |
|
|
\[
{}1-y^{2} \cos \left (t y\right )+\left (t y \cos \left (t y\right )+\sin \left (t y\right )\right ) y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
58.122 |
|
|
\[
{}2 t \sin \left (y\right )-2 t y \sin \left (t^{2}\right )+\left (t^{2} \cos \left (y\right )+\cos \left (t^{2}\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
36.082 |
|
|
\[
{}\left (t +3\right ) \cos \left (y+t \right )+\sin \left (y+t \right )+\left (t +3\right ) \cos \left (y+t \right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
22.535 |
|
|
\[
{}\frac {2 t^{2} y \cos \left (t^{2}\right )-y \sin \left (t^{2}\right )}{t^{2}}+\frac {\left (2 t y+\sin \left (t^{2}\right )\right ) y^{\prime }}{t} = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
8.989 |
|
|
\[
{}-\frac {y^{2} {\mathrm e}^{\frac {y}{t}}}{t^{2}}+1+{\mathrm e}^{\frac {y}{t}} \left (1+\frac {y}{t}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
5.487 |
|
|
\[
{}2 t \sin \left (\frac {y}{t}\right )-y \cos \left (\frac {y}{t}\right )+t \cos \left (\frac {y}{t}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
4.610 |
|
|
\[
{}2 t y^{2}+2 t^{2} y y^{\prime } = 0
\] |
[_separable] |
✓ |
3.013 |
|
|
\[
{}1+\frac {y}{t^{2}}-\frac {y^{\prime }}{t} = 0
\] |
[_linear] |
✓ |
1.972 |
|
|
\[
{}2 t y+3 t^{2}+\left (t^{2}-1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.555 |
|
|
\[
{}1+5 t -y-\left (t +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.038 |
|
|
\[
{}{\mathrm e}^{y}-2 t y+\left (t \,{\mathrm e}^{y}-t^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
1.862 |
|
|
\[
{}2 t y \,{\mathrm e}^{t^{2}}+2 t \,{\mathrm e}^{-y}+\left ({\mathrm e}^{t^{2}}-t^{2} {\mathrm e}^{-y}+1\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
36.272 |
|
|
\[
{}y^{2}-2 \sin \left (2 t \right )+\left (1+2 t y\right ) y^{\prime } = 0
\] |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
43.838 |
|
|
\[
{}\cos \left (t \right )^{2}-\sin \left (t \right )^{2}+y+\left (\sec \left (y\right ) \tan \left (y\right )+t \right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
39.026 |
|
|
\[
{}\frac {1}{t^{2}+1}-y^{2}-2 t y y^{\prime } = 0
\] |
[_exact, _rational, _Bernoulli] |
✓ |
4.217 |
|
|
\[
{}\frac {2 t}{t^{2}+1}+y+\left ({\mathrm e}^{y}+t \right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
3.007 |
|
|
\[
{}-2 x -y \cos \left (x y\right )+\left (2 y-x \cos \left (x y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
9.494 |
|
|
\[
{}-4 x^{3}+6 y \sin \left (6 x y\right )+\left (4 y^{3}+6 x \sin \left (6 x y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
41.687 |
|
|
\[
{}t^{2} y+t^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.217 |
|
|
\[
{}y \left (2 \,{\mathrm e}^{t}+4 t \right )+3 \left ({\mathrm e}^{t}+t^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.278 |
|
|
\[
{}y+\left (2 t -y \,{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.276 |
|
|
\[
{}2 t y+y^{2}-t^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.825 |
|
|
\[
{}y+2 t^{2}+\left (t^{2} y-t \right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.345 |
|
|
\[
{}5 t y+4 y^{2}+1+\left (t^{2}+2 t y\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.538 |
|
|
\[
{}5 t y^{2}+y+\left (2 t^{3}-t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
3.451 |
|
|
\[
{}2 t +\tan \left (y\right )+\left (t -t^{2} \tan \left (y\right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.426 |
|
|
\[
{}2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
38.506 |
|
|
\[
{}-1+{\mathrm e}^{t y} y+y \cos \left (t y\right )+\left (1+{\mathrm e}^{t y} t +t \cos \left (t y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
37.396 |
|
|
\[
{}2 t +2 y+\left (2 t +2 y\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
1.011 |
|
|
\[
{}\frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.382 |
|
|
\[
{}2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.671 |
|
|
\[
{}y^{\prime }-\frac {y}{2} = \frac {t}{y}
\] |
[_rational, _Bernoulli] |
✓ |
1.397 |
|
|
\[
{}y^{\prime }+y = t y^{2}
\] |
[_Bernoulli] |
✓ |
1.396 |
|
|
\[
{}2 y^{\prime } t -y = 2 t y^{3} \cos \left (t \right )
\] |
[_Bernoulli] |
✓ |
40.532 |
|
|
\[
{}y^{\prime } t -y = t y^{3} \sin \left (t \right )
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
40.572 |
|
|
\[
{}y^{\prime }-2 y = \frac {\cos \left (t \right )}{\sqrt {y}}
\] |
[_Bernoulli] |
✓ |
20.766 |
|
|
\[
{}y^{\prime }+3 y = \sqrt {y}\, \sin \left (t \right )
\] |
[_Bernoulli] |
✓ |
1.886 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = t y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.329 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.471 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t}
\] |
[_separable] |
✓ |
2.189 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = t^{2} y^{{3}/{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
4.734 |
|
|
\[
{}\cos \left (\frac {t}{y+t}\right )+{\mathrm e}^{\frac {2 y}{t}} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
20.595 |
|
|
\[
{}y \ln \left (\frac {t}{y}\right )+\frac {t^{2} y^{\prime }}{y+t} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.454 |
|
|
\[
{}2 \ln \left (t \right )-\ln \left (4 y^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
10.868 |
|
|
\[
{}\frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
3.192 |
|
|
\[
{}\frac {\sin \left (2 t \right )}{\cos \left (2 y\right )}+\frac {\ln \left (y\right ) y^{\prime }}{\ln \left (t \right )} = 0
\] |
[_separable] |
✓ |
8.309 |
|
|
\[
{}\sqrt {t^{2}+1}+y y^{\prime } = 0
\] |
[_separable] |
✓ |
1.645 |
|
|
\[
{}2 t +\left (y-3 t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
6.928 |
|
|
\[
{}2 y-3 t +y^{\prime } t = 0
\] |
[_linear] |
✓ |
2.558 |
|
|
\[
{}t y-y^{2}+t \left (t -3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.882 |
|
|
\[
{}t^{2}+t y+y^{2}-t y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.287 |
|
|
\[
{}t^{3}+y^{3}-t y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
8.359 |
|
|
\[
{}y^{\prime } = \frac {t +4 y}{4 t +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.909 |
|
|
\[
{}t -y+y^{\prime } t = 0
\] |
[_linear] |
✓ |
1.593 |
|
|
\[
{}y+\left (y+t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.280 |
|
|
\[
{}2 t^{2}-7 t y+5 y^{2}+t y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
6.844 |
|
|
\[
{}y+2 \sqrt {t^{2}+y^{2}}-y^{\prime } t = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
10.515 |
|
|
\[
{}y^{2} = \left (t y-4 t^{2}\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
5.946 |
|
|
\[
{}y-\left (3 \sqrt {t y}+t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
10.310 |
|
|
\[
{}\left (t^{2}-y^{2}\right ) y^{\prime }+y^{2}+t y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.696 |
|
|
\[
{}t y y^{\prime }-t^{2} {\mathrm e}^{-\frac {y}{t}}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.226 |
|
|
\[
{}y^{\prime } = \frac {1}{\frac {2 y \,{\mathrm e}^{-\frac {t}{y}}}{t}+\frac {t}{y}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.257 |
|
|
\[
{}t \left (\ln \left (t \right )-\ln \left (y\right )\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
7.543 |
|