|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y+\left (y+t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.148 |
|
|
\[
{}2 t^{2}-7 t y+5 y^{2}+t y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
14.556 |
|
|
\[
{}y+2 \sqrt {t^{2}+y^{2}}-t y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
9.286 |
|
|
\[
{}y^{2} = \left (t y-4 t^{2}\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
5.534 |
|
|
\[
{}y-\left (3 \sqrt {t y}+t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
11.293 |
|
|
\[
{}\left (t^{2}-y^{2}\right ) y^{\prime }+y^{2}+t y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.362 |
|
|
\[
{}t y y^{\prime }-t^{2} {\mathrm e}^{-\frac {y}{t}}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.028 |
|
|
\[
{}y^{\prime } = \frac {1}{\frac {2 y \,{\mathrm e}^{-\frac {t}{y}}}{t}+\frac {t}{y}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.039 |
|
|
\[
{}t \left (\ln \left (t \right )-\ln \left (y\right )\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.209 |
|
|
\[
{}y^{\prime }+2 y = t^{2} \sqrt {y}
\] |
[_Bernoulli] |
✓ |
1.297 |
|
|
\[
{}y^{\prime }-2 y = t^{2} \sqrt {y}
\] |
[_Bernoulli] |
✓ |
1.419 |
|
|
\[
{}y^{\prime } = \frac {4 y^{2}-t^{2}}{2 t y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.486 |
|
|
\[
{}t +y-t y^{\prime } = 0
\] |
[_linear] |
✓ |
1.775 |
|
|
\[
{}t y^{\prime }-y-\sqrt {t^{2}+y^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.278 |
|
|
\[
{}t^{3}+y^{2} \sqrt {t^{2}+y^{2}}-t y \sqrt {t^{2}+y^{2}}\, y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
334.595 |
|
|
\[
{}y^{3}-t^{3}-t y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
112.735 |
|
|
\[
{}t y^{3}-\left (t^{4}+y^{4}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
17.997 |
|
|
\[
{}y^{4}+\left (t^{4}-t y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✗ |
7.453 |
|
|
\[
{}t -2 y+1+\left (4 t -3 y-6\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.675 |
|
|
\[
{}5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.266 |
|
|
\[
{}3 t -y+1-\left (6 t -2 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.836 |
|
|
\[
{}2 t +3 y+1+\left (4 t +6 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.824 |
|
|
\[
{}y^{\prime }-\frac {2 y}{x} = -x^{2} y
\] |
[_separable] |
✓ |
1.707 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = y^{4}
\] |
[_Bernoulli] |
✓ |
3.221 |
|
|
\[
{}t y^{\prime }-{y^{\prime }}^{3} = y
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.451 |
|
|
\[
{}t y^{\prime }-y-2 \left (t y^{\prime }-y\right )^{2} = y^{\prime }+1
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.675 |
|
|
\[
{}t y^{\prime }-y-1 = {y^{\prime }}^{2}-y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.456 |
|
|
\[
{}1+y-t y^{\prime } = \ln \left (y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.796 |
|
|
\[
{}1-2 t y^{\prime }+2 y = \frac {1}{{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.735 |
|
|
\[
{}y = -t y^{\prime }+\frac {{y^{\prime }}^{5}}{5}
\] |
[_dAlembert] |
✓ |
0.607 |
|
|
\[
{}y = t {y^{\prime }}^{2}+3 {y^{\prime }}^{2}-2 {y^{\prime }}^{3}
\] |
[_dAlembert] |
✓ |
10.223 |
|
|
\[
{}y = t \left (y^{\prime }+1\right )+2 y^{\prime }+1
\] |
[_linear] |
✓ |
1.376 |
|
|
\[
{}y = t \left (2-y^{\prime }\right )+2 {y^{\prime }}^{2}+1
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.470 |
|
|
\[
{}t^{{1}/{3}} y^{{2}/{3}}+t +\left (t^{{2}/{3}} y^{{1}/{3}}+y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
37.163 |
|
|
\[
{}y^{\prime } = \frac {y^{2}-t^{2}}{t y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.656 |
|
|
\[
{}y \sin \left (\frac {t}{y}\right )-\left (t +t \sin \left (\frac {t}{y}\right )\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
16.721 |
|
|
\[
{}y^{\prime } = \frac {2 t^{5}}{5 y^{2}}
\] |
[_separable] |
✓ |
2.402 |
|
|
\[
{}\cos \left (4 x \right )-8 \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.757 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t}
\] |
[_separable] |
✓ |
2.269 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{8 y}}{t}
\] |
[_separable] |
✓ |
1.662 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{5 t}}{y^{4}}
\] |
[_separable] |
✓ |
1.439 |
|
|
\[
{}-\frac {1}{x^{5}}+\frac {1}{x^{3}} = \left (2 y^{4}-6 y^{9}\right ) y^{\prime }
\] |
[_separable] |
✓ |
1.714 |
|
|
\[
{}y^{\prime } = \frac {y \,{\mathrm e}^{-2 t}}{\ln \left (y\right )}
\] |
[_separable] |
✓ |
1.411 |
|
|
\[
{}y^{\prime } = \frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (x -1\right ) \left (2 x -5\right )}
\] |
[_separable] |
✓ |
1.928 |
|
|
\[
{}y^{\prime }+3 y = -10 \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.351 |
|
|
\[
{}3 t +\left (t -4 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
5.308 |
|
|
\[
{}y-t +\left (y+t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.621 |
|
|
\[
{}y-x +y^{\prime } = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
1.161 |
|
|
\[
{}y^{2}+\left (t y+t^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
6.101 |
|
|
\[
{}r^{\prime } = \frac {r^{2}+t^{2}}{r t}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.619 |
|
|
\[
{}x^{\prime } = \frac {5 t x}{t^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
25.845 |
|
|
\[
{}t^{2}-y+\left (y-t \right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.124 |
|
|
\[
{}t^{2} y+\sin \left (t \right )+\left (\frac {t^{3}}{3}-\cos \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
4.108 |
|
|
\[
{}\tan \left (y\right )-t +\left (t \sec \left (y\right )^{2}+1\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
3.750 |
|
|
\[
{}t \ln \left (y\right )+\left (\frac {t^{2}}{2 y}+1\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.306 |
|
|
\[
{}y^{\prime }+y = 5
\] |
[_quadrature] |
✓ |
1.160 |
|
|
\[
{}y^{\prime }+t y = t
\] |
[_separable] |
✓ |
1.661 |
|
|
\[
{}x^{\prime }+\frac {x}{y} = y^{2}
\] |
[_linear] |
✓ |
1.526 |
|
|
\[
{}t r^{\prime }+r = t \cos \left (t \right )
\] |
[_linear] |
✓ |
1.312 |
|
|
\[
{}y^{\prime }-y = t y^{3}
\] |
[_Bernoulli] |
✓ |
2.318 |
|
|
\[
{}y^{\prime }+y = \frac {{\mathrm e}^{t}}{y^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
2.102 |
|
|
\[
{}y = t y^{\prime }+3 {y^{\prime }}^{4}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.139 |
|
|
\[
{}y-t y^{\prime } = 2 y^{2} \ln \left (t \right )
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
2.603 |
|
|
\[
{}y-t y^{\prime } = -2 {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.453 |
|
|
\[
{}y-t y^{\prime } = -4 {y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.320 |
|
|
\[
{}2 x -y-2+\left (2 y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
10.810 |
|
|
\[
{}\cos \left (t -y\right )+\left (1-\cos \left (t -y\right )\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
123.088 |
|
|
\[
{}{\mathrm e}^{t y} y-2 t +t \,{\mathrm e}^{t y} y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.758 |
|
|
\[
{}\sin \left (y\right )-y \cos \left (t \right )+\left (t \cos \left (y\right )-\sin \left (t \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
8.680 |
|
|
\[
{}y^{2}+\left (2 t y-2 \cos \left (y\right ) \sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.028 |
|
|
\[
{}\frac {y}{t}+\ln \left (y\right )+\left (\frac {t}{y}+\ln \left (t \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.011 |
|
|
\[
{}y^{\prime } = y^{2}-x
\] |
[[_Riccati, _special]] |
✓ |
17.055 |
|
|
\[
{}y^{\prime } = \sqrt {x -y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.152 |
|
|
\[
{}y^{\prime } = t y^{3}
\] |
[_separable] |
✓ |
3.522 |
|
|
\[
{}y^{\prime } = \frac {t}{y^{3}}
\] |
[_separable] |
✓ |
5.102 |
|
|
\[
{}y^{\prime } = -\frac {y}{t -2}
\] |
[_separable] |
✓ |
2.416 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.189 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.179 |
|
|
\[
{}2 t^{2} y^{\prime \prime }-3 t y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.047 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.220 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.650 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.069 |
|
|
\[
{}3 t^{2} y^{\prime \prime }-5 t y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.830 |
|
|
\[
{}t^{2} y^{\prime \prime }+7 t y^{\prime }-7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.709 |
|
|
\[
{}y^{\prime \prime }+y = 2 \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.697 |
|
|
\[
{}y^{\prime \prime }+10 y^{\prime }+24 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.065 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.276 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+18 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.915 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.226 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.471 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.475 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.552 |
|
|
\[
{}y^{\prime \prime }+10 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.459 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.651 |
|
|
\[
{}y^{\prime \prime }+49 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.520 |
|
|
\[
{}t^{2} y^{\prime \prime }+4 t y^{\prime }-4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.305 |
|
|
\[
{}t^{2} y^{\prime \prime }+6 t y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.305 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.354 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.309 |
|
|
\[
{}a y^{\prime \prime }+b y^{\prime }+c y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.692 |
|