|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 t y+\left (t^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
3.271 |
|
|
\[
{}2 t y^{3}+\left (1+3 t^{2} y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
1.482 |
|
|
\[
{}\sin \left (y\right )^{2}+t \sin \left (2 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
4.425 |
|
|
\[
{}3 t^{2}+3 y^{2}+6 t y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
3.956 |
|
|
\[
{}{\mathrm e}^{t} \sin \left (y\right )+\left (1+{\mathrm e}^{t} \cos \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.978 |
|
|
\[
{}3 t^{2} y+3 y^{2}-1+\left (t^{3}+6 t y\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.384 |
|
|
\[
{}-2 t y^{2} \sin \left (t^{2}\right )+2 y \cos \left (t^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.964 |
|
|
\[
{}2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
72.355 |
|
|
\[
{}1-y^{2} \cos \left (t y\right )+\left (t y \cos \left (t y\right )+\sin \left (t y\right )\right ) y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
85.223 |
|
|
\[
{}2 t \sin \left (y\right )-2 t y \sin \left (t^{2}\right )+\left (t^{2} \cos \left (y\right )+\cos \left (t^{2}\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
69.061 |
|
|
\[
{}\left (3+t \right ) \cos \left (y+t \right )+\sin \left (y+t \right )+\left (3+t \right ) \cos \left (y+t \right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
47.938 |
|
|
\[
{}\frac {2 t^{2} y \cos \left (t^{2}\right )-y \sin \left (t^{2}\right )}{t^{2}}+\frac {\left (2 t y+\sin \left (t^{2}\right )\right ) y^{\prime }}{t} = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
12.832 |
|
|
\[
{}-\frac {y^{2} {\mathrm e}^{\frac {y}{t}}}{t^{2}}+1+{\mathrm e}^{\frac {y}{t}} \left (1+\frac {y}{t}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
4.895 |
|
|
\[
{}2 t \sin \left (\frac {y}{t}\right )-y \cos \left (\frac {y}{t}\right )+t \cos \left (\frac {y}{t}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
4.217 |
|
|
\[
{}2 t y^{2}+2 t^{2} y y^{\prime } = 0
\] |
[_separable] |
✓ |
1.780 |
|
|
\[
{}1+\frac {y}{t^{2}}-\frac {y^{\prime }}{t} = 0
\] |
[_linear] |
✓ |
1.252 |
|
|
\[
{}2 t y+3 t^{2}+\left (t^{2}-1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.214 |
|
|
\[
{}1+5 t -y-\left (t +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.061 |
|
|
\[
{}{\mathrm e}^{y}-2 t y+\left (t \,{\mathrm e}^{y}-t^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
1.553 |
|
|
\[
{}2 t y \,{\mathrm e}^{t^{2}}+2 t \,{\mathrm e}^{-y}+\left ({\mathrm e}^{t^{2}}-t^{2} {\mathrm e}^{-y}+1\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
70.217 |
|
|
\[
{}y^{2}-2 \sin \left (2 t \right )+\left (1+2 t y\right ) y^{\prime } = 0
\] |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
96.254 |
|
|
\[
{}\cos \left (t \right )^{2}-\sin \left (t \right )^{2}+y+\left (\sec \left (y\right ) \tan \left (y\right )+t \right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
71.395 |
|
|
\[
{}\frac {1}{t^{2}+1}-y^{2}-2 t y y^{\prime } = 0
\] |
[_exact, _rational, _Bernoulli] |
✓ |
1.564 |
|
|
\[
{}\frac {2 t}{t^{2}+1}+y+\left ({\mathrm e}^{y}+t \right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
1.868 |
|
|
\[
{}-2 x -y \cos \left (y x \right )+\left (2 y-x \cos \left (y x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
15.973 |
|
|
\[
{}-4 x^{3}+6 y \sin \left (6 y x \right )+\left (4 y^{3}+6 x \sin \left (6 y x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
88.545 |
|
|
\[
{}t^{2} y+t^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.433 |
|
|
\[
{}y \left (2 \,{\mathrm e}^{t}+4 t \right )+3 \left ({\mathrm e}^{t}+t^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.733 |
|
|
\[
{}y+\left (2 t -y \,{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.110 |
|
|
\[
{}2 t y+y^{2}-t^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
1.937 |
|
|
\[
{}y+2 t^{2}+\left (t^{2} y-t \right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.152 |
|
|
\[
{}5 t y+4 y^{2}+1+\left (t^{2}+2 t y\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.341 |
|
|
\[
{}5 t y^{2}+y+\left (2 t^{3}-t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
3.270 |
|
|
\[
{}2 t +\tan \left (y\right )+\left (t -t^{2} \tan \left (y\right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.120 |
|
|
\[
{}2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
73.141 |
|
|
\[
{}-1+{\mathrm e}^{t y} y+y \cos \left (t y\right )+\left (1+{\mathrm e}^{t y} t +t \cos \left (t y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
73.326 |
|
|
\[
{}2 t +2 y+\left (2 t +2 y\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.464 |
|
|
\[
{}\frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.827 |
|
|
\[
{}2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.184 |
|
|
\[
{}y^{\prime }-\frac {y}{2} = \frac {t}{y}
\] |
[_rational, _Bernoulli] |
✓ |
1.158 |
|
|
\[
{}y^{\prime }+y = t y^{2}
\] |
[_Bernoulli] |
✓ |
1.286 |
|
|
\[
{}2 t y^{\prime }-y = 2 t y^{3} \cos \left (t \right )
\] |
[_Bernoulli] |
✓ |
80.326 |
|
|
\[
{}t y^{\prime }-y = t y^{3} \sin \left (t \right )
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
78.557 |
|
|
\[
{}y^{\prime }-2 y = \frac {\cos \left (t \right )}{\sqrt {y}}
\] |
[_Bernoulli] |
✓ |
40.132 |
|
|
\[
{}y^{\prime }+3 y = \sqrt {y}\, \sin \left (t \right )
\] |
[_Bernoulli] |
✓ |
1.793 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = t y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
1.829 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
1.827 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t}
\] |
[_separable] |
✓ |
1.558 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = t^{2} y^{{3}/{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
4.419 |
|
|
\[
{}\cos \left (\frac {t}{y+t}\right )+{\mathrm e}^{\frac {2 y}{t}} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
18.810 |
|
|
\[
{}y \ln \left (\frac {t}{y}\right )+\frac {t^{2} y^{\prime }}{y+t} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.613 |
|
|
\[
{}2 \ln \left (t \right )-\ln \left (4 y^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
11.292 |
|
|
\[
{}\frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.431 |
|
|
\[
{}\frac {\sin \left (2 t \right )}{\cos \left (2 y\right )}+\frac {\ln \left (y\right ) y^{\prime }}{\ln \left (t \right )} = 0
\] |
[_separable] |
✓ |
13.969 |
|
|
\[
{}\sqrt {t^{2}+1}+y y^{\prime } = 0
\] |
[_separable] |
✓ |
1.306 |
|
|
\[
{}2 t +\left (y-3 t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
5.575 |
|
|
\[
{}2 y-3 t +t y^{\prime } = 0
\] |
[_linear] |
✓ |
1.688 |
|
|
\[
{}t y-y^{2}+t \left (t -3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.074 |
|
|
\[
{}t^{2}+t y+y^{2}-t y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
36.331 |
|
|
\[
{}t^{3}+y^{3}-t y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.254 |
|
|
\[
{}y^{\prime } = \frac {t +4 y}{4 t +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.299 |
|
|
\[
{}t -y+t y^{\prime } = 0
\] |
[_linear] |
✓ |
1.086 |
|
|
\[
{}y+\left (y+t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.150 |
|
|
\[
{}2 t^{2}-7 t y+5 y^{2}+t y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
6.286 |
|
|
\[
{}y+2 \sqrt {t^{2}+y^{2}}-t y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
9.104 |
|
|
\[
{}y^{2} = \left (t y-4 t^{2}\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
40.080 |
|
|
\[
{}y-\left (3 \sqrt {t y}+t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
10.121 |
|
|
\[
{}\left (t^{2}-y^{2}\right ) y^{\prime }+y^{2}+t y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.532 |
|
|
\[
{}t y y^{\prime }-t^{2} {\mathrm e}^{-\frac {y}{t}}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
2.550 |
|
|
\[
{}y^{\prime } = \frac {1}{\frac {2 y \,{\mathrm e}^{-\frac {t}{y}}}{t}+\frac {t}{y}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.433 |
|
|
\[
{}t \left (\ln \left (t \right )-\ln \left (y\right )\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.918 |
|
|
\[
{}y^{\prime }+2 y = t^{2} \sqrt {y}
\] |
[_Bernoulli] |
✓ |
1.456 |
|
|
\[
{}y^{\prime }-2 y = t^{2} \sqrt {y}
\] |
[_Bernoulli] |
✗ |
4.285 |
|
|
\[
{}y^{\prime } = \frac {4 y^{2}-t^{2}}{2 t y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.212 |
|
|
\[
{}t +y-t y^{\prime } = 0
\] |
[_linear] |
✓ |
1.336 |
|
|
\[
{}t y^{\prime }-y-\sqrt {t^{2}+y^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.023 |
|
|
\[
{}t^{3}+y^{2} \sqrt {t^{2}+y^{2}}-t y \sqrt {t^{2}+y^{2}}\, y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.865 |
|
|
\[
{}y^{3}-t^{3}-t y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
67.059 |
|
|
\[
{}t y^{3}-\left (t^{4}+y^{4}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
12.252 |
|
|
\[
{}y^{4}+\left (t^{4}-t y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✗ |
5.608 |
|
|
\[
{}t -2 y+1+\left (4 t -3 y-6\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.691 |
|
|
\[
{}5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.358 |
|
|
\[
{}3 t -y+1-\left (6 t -2 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.200 |
|
|
\[
{}2 t +3 y+1+\left (4 t +6 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.320 |
|
|
\[
{}y^{\prime }-\frac {2 y}{x} = -x^{2} y
\] |
[_separable] |
✓ |
1.178 |
|
|
\[
{}y^{\prime }+\cot \left (x \right ) y = y^{4}
\] |
[_Bernoulli] |
✓ |
3.211 |
|
|
\[
{}t y^{\prime }-{y^{\prime }}^{3} = y
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.381 |
|
|
\[
{}t y^{\prime }-y-2 \left (t y^{\prime }-y\right )^{2} = y^{\prime }+1
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.628 |
|
|
\[
{}t y^{\prime }-y-1 = {y^{\prime }}^{2}-y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.350 |
|
|
\[
{}1+y-t y^{\prime } = \ln \left (y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.631 |
|
|
\[
{}1-2 t y^{\prime }+2 y = \frac {1}{{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.751 |
|
|
\[
{}y = -t y^{\prime }+\frac {{y^{\prime }}^{5}}{5}
\] |
[_dAlembert] |
✓ |
0.595 |
|
|
\[
{}y = t {y^{\prime }}^{2}+3 {y^{\prime }}^{2}-2 {y^{\prime }}^{3}
\] |
[_dAlembert] |
✓ |
10.349 |
|
|
\[
{}y = t \left (y^{\prime }+1\right )+2 y^{\prime }+1
\] |
[_linear] |
✓ |
1.017 |
|
|
\[
{}y = t \left (2-y^{\prime }\right )+2 {y^{\prime }}^{2}+1
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.445 |
|
|
\[
{}t^{{1}/{3}} y^{{2}/{3}}+t +\left (t^{{2}/{3}} y^{{1}/{3}}+y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
70.570 |
|
|
\[
{}y^{\prime } = \frac {y^{2}-t^{2}}{t y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.275 |
|
|
\[
{}y \sin \left (\frac {t}{y}\right )-\left (t +t \sin \left (\frac {t}{y}\right )\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
17.109 |
|
|
\[
{}y^{\prime } = \frac {2 t^{5}}{5 y^{2}}
\] |
[_separable] |
✓ |
2.010 |
|
|
\[
{}\cos \left (4 x \right )-8 \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.254 |
|