|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 t y^{\prime }-y = 2 t y^{3} \cos \left (t \right )
\] |
[_Bernoulli] |
✓ |
40.951 |
|
|
\[
{}t y^{\prime }-y = t y^{3} \sin \left (t \right )
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
41.560 |
|
|
\[
{}y^{\prime }-2 y = \frac {\cos \left (t \right )}{\sqrt {y}}
\] |
[_Bernoulli] |
✓ |
30.435 |
|
|
\[
{}y^{\prime }+3 y = \sqrt {y}\, \sin \left (t \right )
\] |
[_Bernoulli] |
✓ |
2.107 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = t y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.448 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.481 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t}
\] |
[_separable] |
✓ |
2.570 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = t^{2} y^{{3}/{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
7.844 |
|
|
\[
{}\cos \left (\frac {t}{y+t}\right )+{\mathrm e}^{\frac {2 y}{t}} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
39.604 |
|
|
\[
{}y \ln \left (\frac {t}{y}\right )+\frac {t^{2} y^{\prime }}{y+t} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.830 |
|
|
\[
{}2 \ln \left (t \right )-\ln \left (4 y^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
12.642 |
|
|
\[
{}\frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
3.233 |
|
|
\[
{}\frac {\sin \left (2 t \right )}{\cos \left (2 y\right )}+\frac {\ln \left (y\right ) y^{\prime }}{\ln \left (t \right )} = 0
\] |
[_separable] |
✓ |
9.560 |
|
|
\[
{}\sqrt {t^{2}+1}+y y^{\prime } = 0
\] |
[_separable] |
✓ |
2.284 |
|
|
\[
{}2 t +\left (y-3 t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
8.230 |
|
|
\[
{}2 y-3 t +t y^{\prime } = 0
\] |
[_linear] |
✓ |
2.545 |
|
|
\[
{}t y-y^{2}+t \left (t -3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
105.707 |
|
|
\[
{}t^{2}+t y+y^{2}-t y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
38.277 |
|
|
\[
{}t^{3}+y^{3}-t y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
12.103 |
|
|
\[
{}y^{\prime } = \frac {t +4 y}{4 t +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.061 |
|
|
\[
{}t -y+t y^{\prime } = 0
\] |
[_linear] |
✓ |
1.628 |
|
|
\[
{}y+\left (y+t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.206 |
|
|
\[
{}2 t^{2}-7 t y+5 y^{2}+t y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
99.068 |
|
|
\[
{}y+2 \sqrt {t^{2}+y^{2}}-t y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
12.405 |
|
|
\[
{}y^{2} = \left (t y-4 t^{2}\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
45.946 |
|
|
\[
{}y-\left (3 \sqrt {t y}+t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
17.124 |
|
|
\[
{}\left (t^{2}-y^{2}\right ) y^{\prime }+y^{2}+t y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.664 |
|
|
\[
{}t y y^{\prime }-t^{2} {\mathrm e}^{-\frac {y}{t}}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.418 |
|
|
\[
{}y^{\prime } = \frac {1}{\frac {2 y \,{\mathrm e}^{-\frac {t}{y}}}{t}+\frac {t}{y}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.597 |
|
|
\[
{}t \left (\ln \left (t \right )-\ln \left (y\right )\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
11.352 |
|
|
\[
{}y^{\prime }+2 y = t^{2} \sqrt {y}
\] |
[_Bernoulli] |
✓ |
1.596 |
|
|
\[
{}y^{\prime }-2 y = t^{2} \sqrt {y}
\] |
[_Bernoulli] |
✓ |
1.697 |
|
|
\[
{}y^{\prime } = \frac {4 y^{2}-t^{2}}{2 t y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
98.895 |
|
|
\[
{}t +y-t y^{\prime } = 0
\] |
[_linear] |
✓ |
2.115 |
|
|
\[
{}t y^{\prime }-y-\sqrt {t^{2}+y^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.618 |
|
|
\[
{}t^{3}+y^{2} \sqrt {t^{2}+y^{2}}-t y \sqrt {t^{2}+y^{2}}\, y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
591.126 |
|
|
\[
{}y^{3}-t^{3}-t y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
220.162 |
|
|
\[
{}t y^{3}-\left (t^{4}+y^{4}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
20.815 |
|
|
\[
{}y^{4}+\left (t^{4}-t y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
10.454 |
|
|
\[
{}t -2 y+1+\left (4 t -3 y-6\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.744 |
|
|
\[
{}5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.375 |
|
|
\[
{}3 t -y+1-\left (6 t -2 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.195 |
|
|
\[
{}2 t +3 y+1+\left (4 t +6 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.224 |
|
|
\[
{}y^{\prime }-\frac {2 y}{x} = -x^{2} y
\] |
[_separable] |
✓ |
1.891 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = y^{4}
\] |
[_Bernoulli] |
✓ |
3.576 |
|
|
\[
{}t y^{\prime }-{y^{\prime }}^{3} = y
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.436 |
|
|
\[
{}t y^{\prime }-y-2 \left (t y^{\prime }-y\right )^{2} = y^{\prime }+1
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.812 |
|
|
\[
{}t y^{\prime }-y-1 = {y^{\prime }}^{2}-y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.481 |
|
|
\[
{}1+y-t y^{\prime } = \ln \left (y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.177 |
|
|
\[
{}1-2 t y^{\prime }+2 y = \frac {1}{{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.903 |
|
|
\[
{}y = -t y^{\prime }+\frac {{y^{\prime }}^{5}}{5}
\] |
[_dAlembert] |
✓ |
1.167 |
|
|
\[
{}y = t {y^{\prime }}^{2}+3 {y^{\prime }}^{2}-2 {y^{\prime }}^{3}
\] |
[_dAlembert] |
✓ |
12.245 |
|
|
\[
{}y = t \left (y^{\prime }+1\right )+2 y^{\prime }+1
\] |
[_linear] |
✓ |
1.484 |
|
|
\[
{}y = t \left (2-y^{\prime }\right )+2 {y^{\prime }}^{2}+1
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.519 |
|
|
\[
{}t^{{1}/{3}} y^{{2}/{3}}+t +\left (t^{{2}/{3}} y^{{1}/{3}}+y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
51.906 |
|
|
\[
{}y^{\prime } = \frac {y^{2}-t^{2}}{t y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
9.406 |
|
|
\[
{}y \sin \left (\frac {t}{y}\right )-\left (t +t \sin \left (\frac {t}{y}\right )\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
8.000 |
|
|
\[
{}y^{\prime } = \frac {2 t^{5}}{5 y^{2}}
\] |
[_separable] |
✓ |
2.618 |
|
|
\[
{}\cos \left (4 x \right )-8 \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.343 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t}
\] |
[_separable] |
✓ |
2.560 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{8 y}}{t}
\] |
[_separable] |
✓ |
1.802 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{5 t}}{y^{4}}
\] |
[_separable] |
✓ |
1.620 |
|
|
\[
{}-\frac {1}{x^{5}}+\frac {1}{x^{3}} = \left (2 y^{4}-6 y^{9}\right ) y^{\prime }
\] |
[_separable] |
✓ |
2.094 |
|
|
\[
{}y^{\prime } = \frac {y \,{\mathrm e}^{-2 t}}{\ln \left (y\right )}
\] |
[_separable] |
✓ |
1.715 |
|
|
\[
{}y^{\prime } = \frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (-1+x \right ) \left (2 x -5\right )}
\] |
[_separable] |
✓ |
2.285 |
|
|
\[
{}y^{\prime }+3 y = -10 \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.592 |
|
|
\[
{}3 t +\left (t -4 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
4.382 |
|
|
\[
{}y-t +\left (y+t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.508 |
|
|
\[
{}y-x +y^{\prime } = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
1.247 |
|
|
\[
{}y^{2}+\left (t y+t^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
146.656 |
|
|
\[
{}r^{\prime } = \frac {r^{2}+t^{2}}{r t}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.098 |
|
|
\[
{}x^{\prime } = \frac {5 t x}{x^{2}+t^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
402.318 |
|
|
\[
{}t^{2}-y+\left (-t +y\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.324 |
|
|
\[
{}t^{2} y+\sin \left (t \right )+\left (\frac {t^{3}}{3}-\cos \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
5.327 |
|
|
\[
{}\tan \left (y\right )-t +\left (t \sec \left (y\right )^{2}+1\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
5.231 |
|
|
\[
{}t \ln \left (y\right )+\left (\frac {t^{2}}{2 y}+1\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.675 |
|
|
\[
{}y^{\prime }+y = 5
\] |
[_quadrature] |
✓ |
1.455 |
|
|
\[
{}y^{\prime }+t y = t
\] |
[_separable] |
✓ |
1.565 |
|
|
\[
{}x^{\prime }+\frac {x}{y} = y^{2}
\] |
[_linear] |
✓ |
1.520 |
|
|
\[
{}t r^{\prime }+r = t \cos \left (t \right )
\] |
[_linear] |
✓ |
1.485 |
|
|
\[
{}y^{\prime }-y = t y^{3}
\] |
[_Bernoulli] |
✓ |
3.027 |
|
|
\[
{}y^{\prime }+y = \frac {{\mathrm e}^{t}}{y^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
2.793 |
|
|
\[
{}y = t y^{\prime }+3 {y^{\prime }}^{4}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.563 |
|
|
\[
{}y-t y^{\prime } = 2 y^{2} \ln \left (t \right )
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
3.085 |
|
|
\[
{}y-t y^{\prime } = -2 {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.426 |
|
|
\[
{}y-t y^{\prime } = -4 {y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.424 |
|
|
\[
{}2 x -y-2+\left (2 y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.372 |
|
|
\[
{}\cos \left (-y+t \right )+\left (1-\cos \left (-y+t \right )\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
115.289 |
|
|
\[
{}{\mathrm e}^{t y} y-2 t +t \,{\mathrm e}^{t y} y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.027 |
|
|
\[
{}\sin \left (y\right )-y \cos \left (t \right )+\left (t \cos \left (y\right )-\sin \left (t \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
9.209 |
|
|
\[
{}y^{2}+\left (2 t y-2 \cos \left (y\right ) \sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.372 |
|
|
\[
{}\frac {y}{t}+\ln \left (y\right )+\left (\frac {t}{y}+\ln \left (t \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.408 |
|
|
\[
{}y^{\prime } = y^{2}-x
\] |
[[_Riccati, _special]] |
✓ |
17.137 |
|
|
\[
{}y^{\prime } = \sqrt {x -y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.880 |
|
|
\[
{}y^{\prime } = t y^{3}
\] |
[_separable] |
✓ |
3.063 |
|
|
\[
{}y^{\prime } = \frac {t}{y^{3}}
\] |
[_separable] |
✓ |
3.840 |
|
|
\[
{}y^{\prime } = -\frac {y}{t -2}
\] |
[_separable] |
✓ |
2.339 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.074 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.973 |
|
|
\[
{}2 t^{2} y^{\prime \prime }-3 t y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.826 |
|