|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}} = 0
\] |
[_separable] |
✓ |
3.042 |
|
|
\[
{}y \cos \left (t y\right )+t \cos \left (t y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.708 |
|
|
\[
{}y \sec \left (t \right )^{2}+2 t +\tan \left (t \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
10.656 |
|
|
\[
{}3 t y^{2}+y^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.013 |
|
|
\[
{}t -\sin \left (t \right ) y+\left (y^{6}+\cos \left (t \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.941 |
|
|
\[
{}y \sin \left (2 t \right )+\left (\sqrt {y}+\cos \left (2 t \right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
6.052 |
|
|
\[
{}\ln \left (t y\right )+\frac {t y^{\prime }}{y} = 0
\] |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
2.056 |
|
|
\[
{}{\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y} = 0
\] |
[_separable] |
✓ |
1.902 |
|
|
\[
{}3 t^{2}-y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.285 |
|
|
\[
{}-1+3 y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
10.645 |
|
|
\[
{}y^{2}+2 t y y^{\prime } = 0
\] |
[_separable] |
✓ |
1.676 |
|
|
\[
{}\frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}} = 0
\] |
[_separable] |
✓ |
1.797 |
|
|
\[
{}2 t +y^{3}+\left (3 t y^{2}+4\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.339 |
|
|
\[
{}-\frac {1}{y}+\left (\frac {t}{y^{2}}+3 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
2.931 |
|
|
\[
{}2 t y+\left (t^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
3.567 |
|
|
\[
{}2 t y^{3}+\left (1+3 t^{2} y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
1.914 |
|
|
\[
{}\sin \left (y\right )^{2}+t \sin \left (2 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
4.904 |
|
|
\[
{}3 t^{2}+3 y^{2}+6 t y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
4.056 |
|
|
\[
{}{\mathrm e}^{t} \sin \left (y\right )+\left (1+{\mathrm e}^{t} \cos \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.016 |
|
|
\[
{}3 t^{2} y+3 y^{2}-1+\left (t^{3}+6 t y\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.503 |
|
|
\[
{}-2 t y^{2} \sin \left (t^{2}\right )+2 y \cos \left (t^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.753 |
|
|
\[
{}2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
38.838 |
|
|
\[
{}1-y^{2} \cos \left (t y\right )+\left (t y \cos \left (t y\right )+\sin \left (t y\right )\right ) y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
59.556 |
|
|
\[
{}2 t \sin \left (y\right )-2 t y \sin \left (t^{2}\right )+\left (t^{2} \cos \left (y\right )+\cos \left (t^{2}\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
35.940 |
|
|
\[
{}\left (3+t \right ) \cos \left (y+t \right )+\sin \left (y+t \right )+\left (3+t \right ) \cos \left (y+t \right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
28.682 |
|
|
\[
{}\frac {2 t^{2} y \cos \left (t^{2}\right )-y \sin \left (t^{2}\right )}{t^{2}}+\frac {\left (2 t y+\sin \left (t^{2}\right )\right ) y^{\prime }}{t} = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
8.774 |
|
|
\[
{}-\frac {y^{2} {\mathrm e}^{\frac {y}{t}}}{t^{2}}+1+{\mathrm e}^{\frac {y}{t}} \left (1+\frac {y}{t}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
5.506 |
|
|
\[
{}2 t \sin \left (\frac {y}{t}\right )-y \cos \left (\frac {y}{t}\right )+t \cos \left (\frac {y}{t}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
4.500 |
|
|
\[
{}2 t y^{2}+2 t^{2} y y^{\prime } = 0
\] |
[_separable] |
✓ |
2.143 |
|
|
\[
{}1+\frac {y}{t^{2}}-\frac {y^{\prime }}{t} = 0
\] |
[_linear] |
✓ |
1.621 |
|
|
\[
{}2 t y+3 t^{2}+\left (t^{2}-1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.394 |
|
|
\[
{}1+5 t -y-\left (t +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.877 |
|
|
\[
{}{\mathrm e}^{y}-2 t y+\left (t \,{\mathrm e}^{y}-t^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
1.941 |
|
|
\[
{}2 t y \,{\mathrm e}^{t^{2}}+2 t \,{\mathrm e}^{-y}+\left ({\mathrm e}^{t^{2}}-t^{2} {\mathrm e}^{-y}+1\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
36.030 |
|
|
\[
{}y^{2}-2 \sin \left (2 t \right )+\left (1+2 t y\right ) y^{\prime } = 0
\] |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
43.499 |
|
|
\[
{}\cos \left (t \right )^{2}-\sin \left (t \right )^{2}+y+\left (\sec \left (y\right ) \tan \left (y\right )+t \right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
38.183 |
|
|
\[
{}\frac {1}{t^{2}+1}-y^{2}-2 t y y^{\prime } = 0
\] |
[_exact, _rational, _Bernoulli] |
✓ |
4.234 |
|
|
\[
{}\frac {2 t}{t^{2}+1}+y+\left ({\mathrm e}^{y}+t \right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.882 |
|
|
\[
{}-2 x -y \cos \left (x y\right )+\left (2 y-x \cos \left (x y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
8.888 |
|
|
\[
{}-4 x^{3}+6 y \sin \left (6 x y\right )+\left (4 y^{3}+6 x \sin \left (6 x y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
43.775 |
|
|
\[
{}t^{2} y+t^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.585 |
|
|
\[
{}y \left (2 \,{\mathrm e}^{t}+4 t \right )+3 \left ({\mathrm e}^{t}+t^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.816 |
|
|
\[
{}y+\left (2 t -y \,{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.175 |
|
|
\[
{}2 t y+y^{2}-t^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.161 |
|
|
\[
{}y+2 t^{2}+\left (t^{2} y-t \right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.222 |
|
|
\[
{}5 t y+4 y^{2}+1+\left (t^{2}+2 t y\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.452 |
|
|
\[
{}5 t y^{2}+y+\left (2 t^{3}-t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
3.105 |
|
|
\[
{}2 t +\tan \left (y\right )+\left (t -t^{2} \tan \left (y\right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.155 |
|
|
\[
{}2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
39.433 |
|
|
\[
{}-1+{\mathrm e}^{t y} y+y \cos \left (t y\right )+\left (1+{\mathrm e}^{t y} t +t \cos \left (t y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
37.049 |
|
|
\[
{}2 t +2 y+\left (2 t +2 y\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.568 |
|
|
\[
{}\frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.870 |
|
|
\[
{}2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.277 |
|
|
\[
{}y^{\prime }-\frac {y}{2} = \frac {t}{y}
\] |
[_rational, _Bernoulli] |
✓ |
1.181 |
|
|
\[
{}y^{\prime }+y = t y^{2}
\] |
[_Bernoulli] |
✓ |
1.435 |
|
|
\[
{}2 t y^{\prime }-y = 2 t y^{3} \cos \left (t \right )
\] |
[_Bernoulli] |
✓ |
41.582 |
|
|
\[
{}t y^{\prime }-y = t y^{3} \sin \left (t \right )
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
40.464 |
|
|
\[
{}y^{\prime }-2 y = \frac {\cos \left (t \right )}{\sqrt {y}}
\] |
[_Bernoulli] |
✓ |
31.732 |
|
|
\[
{}y^{\prime }+3 y = \sqrt {y}\, \sin \left (t \right )
\] |
[_Bernoulli] |
✓ |
1.980 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = t y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
1.888 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
1.753 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t}
\] |
[_separable] |
✓ |
1.829 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = t^{2} y^{{3}/{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
6.607 |
|
|
\[
{}\cos \left (\frac {t}{y+t}\right )+{\mathrm e}^{\frac {2 y}{t}} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
19.551 |
|
|
\[
{}y \ln \left (\frac {t}{y}\right )+\frac {t^{2} y^{\prime }}{y+t} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.951 |
|
|
\[
{}2 \ln \left (t \right )-\ln \left (4 y^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
11.634 |
|
|
\[
{}\frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.687 |
|
|
\[
{}\frac {\sin \left (2 t \right )}{\cos \left (2 y\right )}+\frac {\ln \left (y\right ) y^{\prime }}{\ln \left (t \right )} = 0
\] |
[_separable] |
✓ |
8.267 |
|
|
\[
{}\sqrt {t^{2}+1}+y y^{\prime } = 0
\] |
[_separable] |
✓ |
1.363 |
|
|
\[
{}2 t +\left (y-3 t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
5.068 |
|
|
\[
{}2 y-3 t +t y^{\prime } = 0
\] |
[_linear] |
✓ |
1.934 |
|
|
\[
{}t y-y^{2}+t \left (t -3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.843 |
|
|
\[
{}t^{2}+t y+y^{2}-t y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
36.719 |
|
|
\[
{}t^{3}+y^{3}-t y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.927 |
|
|
\[
{}y^{\prime } = \frac {t +4 y}{4 t +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.093 |
|
|
\[
{}t -y+t y^{\prime } = 0
\] |
[_linear] |
✓ |
1.197 |
|
|
\[
{}y+\left (y+t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.848 |
|
|
\[
{}2 t^{2}-7 t y+5 y^{2}+t y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
12.700 |
|
|
\[
{}y+2 \sqrt {t^{2}+y^{2}}-t y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
10.396 |
|
|
\[
{}y^{2} = \left (t y-4 t^{2}\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
5.200 |
|
|
\[
{}y-\left (3 \sqrt {t y}+t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
11.497 |
|
|
\[
{}\left (t^{2}-y^{2}\right ) y^{\prime }+y^{2}+t y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.862 |
|
|
\[
{}t y y^{\prime }-t^{2} {\mathrm e}^{-\frac {y}{t}}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
2.650 |
|
|
\[
{}y^{\prime } = \frac {1}{\frac {2 y \,{\mathrm e}^{-\frac {t}{y}}}{t}+\frac {t}{y}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.710 |
|
|
\[
{}t \left (\ln \left (t \right )-\ln \left (y\right )\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.344 |
|
|
\[
{}y^{\prime }+2 y = t^{2} \sqrt {y}
\] |
[_Bernoulli] |
✓ |
1.445 |
|
|
\[
{}y^{\prime }-2 y = t^{2} \sqrt {y}
\] |
[_Bernoulli] |
✓ |
1.404 |
|
|
\[
{}y^{\prime } = \frac {4 y^{2}-t^{2}}{2 t y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.273 |
|
|
\[
{}t +y-t y^{\prime } = 0
\] |
[_linear] |
✓ |
1.525 |
|
|
\[
{}t y^{\prime }-y-\sqrt {t^{2}+y^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.262 |
|
|
\[
{}t^{3}+y^{2} \sqrt {t^{2}+y^{2}}-t y \sqrt {t^{2}+y^{2}}\, y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
301.041 |
|
|
\[
{}y^{3}-t^{3}-t y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
93.021 |
|
|
\[
{}t y^{3}-\left (t^{4}+y^{4}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
19.047 |
|
|
\[
{}y^{4}+\left (t^{4}-t y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✗ |
7.707 |
|
|
\[
{}t -2 y+1+\left (4 t -3 y-6\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.437 |
|
|
\[
{}5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.534 |
|
|
\[
{}3 t -y+1-\left (6 t -2 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.451 |
|
|
\[
{}2 t +3 y+1+\left (4 t +6 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.384 |
|
|
\[
{}y^{\prime }-\frac {2 y}{x} = -x^{2} y
\] |
[_separable] |
✓ |
1.352 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = y^{4}
\] |
[_Bernoulli] |
✓ |
3.512 |
|