|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 y^{\prime } y = \frac {x}{\sqrt {x^{2}-4}}
\] |
[_separable] |
✓ |
3.038 |
|
|
\[
{}\sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
38.304 |
|
|
\[
{}y^{2} \sqrt {-x^{2}+1}\, y^{\prime } = \arcsin \left (x \right )
\] |
[_separable] |
✓ |
5.565 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}+1}{12 y^{2}-12 y}
\] |
[_separable] |
✓ |
6.279 |
|
|
\[
{}y^{\prime } = \frac {2 x^{2}}{2 y^{2}-6}
\] |
[_separable] |
✓ |
2.372 |
|
|
\[
{}y^{\prime } = 2 y^{2}+x y^{2}
\] |
[_separable] |
✓ |
1.892 |
|
|
\[
{}y^{\prime } = \frac {6-{\mathrm e}^{x}}{3+2 y}
\] |
[_separable] |
✓ |
3.147 |
|
|
\[
{}y^{\prime } = \frac {2 \cos \left (2 x \right )}{10+2 y}
\] |
[_separable] |
✓ |
4.276 |
|
|
\[
{}y^{\prime } = 2 \left (x +1\right ) \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
2.732 |
|
|
\[
{}y^{\prime } = \frac {t y \left (4-y\right )}{3}
\] |
[_separable] |
✓ |
2.622 |
|
|
\[
{}y^{\prime } = \frac {t y \left (4-y\right )}{t +1}
\] |
[_separable] |
✓ |
3.301 |
|
|
\[
{}y^{\prime } = \frac {a y+b}{c y+d}
\] |
[_quadrature] |
✓ |
1.478 |
|
|
\[
{}y^{\prime }+4 y = t +{\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.206 |
|
|
\[
{}y^{\prime }-2 y = t^{2} {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.501 |
|
|
\[
{}y^{\prime }+y = t \,{\mathrm e}^{-t}+1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.547 |
|
|
\[
{}y^{\prime }+\frac {y}{t} = 5+\cos \left (2 t \right )
\] |
[_linear] |
✓ |
1.628 |
|
|
\[
{}y^{\prime }-2 y = 3 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.109 |
|
|
\[
{}t y^{\prime }+2 y = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.266 |
|
|
\[
{}y^{\prime }+2 t y = 16 t \,{\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
2.291 |
|
|
\[
{}\left (t^{2}+1\right ) y^{\prime }+4 t y = \frac {1}{\left (t^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
2.042 |
|
|
\[
{}2 y^{\prime }+y = 3 t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.033 |
|
|
\[
{}t y^{\prime }-y = t^{3} {\mathrm e}^{-t}
\] |
[_linear] |
✓ |
1.188 |
|
|
\[
{}y^{\prime }+y = 5 \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.367 |
|
|
\[
{}2 y^{\prime }+y = 3 t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.100 |
|
|
\[
{}y^{\prime }-y = 2 t \,{\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.390 |
|
|
\[
{}y^{\prime }+2 y = t \,{\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.879 |
|
|
\[
{}t y^{\prime }+4 y = t^{2}-t +1
\] |
[_linear] |
✓ |
1.580 |
|
|
\[
{}y^{\prime }+\frac {2 y}{t} = \frac {\cos \left (t \right )}{t^{2}}
\] |
[_linear] |
✓ |
1.639 |
|
|
\[
{}y^{\prime }-2 y = {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.312 |
|
|
\[
{}t y^{\prime }+2 y = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.670 |
|
|
\[
{}t^{3} y^{\prime }+4 t^{2} y = {\mathrm e}^{-t}
\] |
[_linear] |
✓ |
1.542 |
|
|
\[
{}t y^{\prime }+\left (t +1\right ) y = t
\] |
[_linear] |
✓ |
1.359 |
|
|
\[
{}y^{\prime }-\frac {y}{3} = 3 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.499 |
|
|
\[
{}2 y^{\prime }-y = {\mathrm e}^{\frac {t}{3}}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.320 |
|
|
\[
{}3 y^{\prime }-2 y = {\mathrm e}^{-\frac {\pi t}{2}}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.478 |
|
|
\[
{}t y^{\prime }+\left (t +1\right ) y = 2 t \,{\mathrm e}^{-t}
\] |
[_linear] |
✓ |
1.938 |
|
|
\[
{}t y^{\prime }+2 y = \frac {\sin \left (t \right )}{t}
\] |
[_linear] |
✓ |
1.439 |
|
|
\[
{}\sin \left (t \right ) y^{\prime }+\cos \left (t \right ) y = {\mathrm e}^{t}
\] |
[_linear] |
✓ |
38.579 |
|
|
\[
{}y^{\prime }+\frac {y}{2} = 2 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.674 |
|
|
\[
{}y^{\prime }+\frac {4 y}{3} = 1-\frac {t}{4}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.264 |
|
|
\[
{}y^{\prime }+\frac {y}{4} = 3+2 \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
2.030 |
|
|
\[
{}y^{\prime }-y = 1+3 \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.596 |
|
|
\[
{}y^{\prime }-\frac {3 y}{2} = 3 t +3 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.482 |
|
|
\[
{}y^{\prime }-6 y = t^{6} {\mathrm e}^{6 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.601 |
|
|
\[
{}y^{\prime }+\frac {y}{t} = 3 \cos \left (2 t \right )
\] |
[_linear] |
✓ |
1.473 |
|
|
\[
{}t y^{\prime }+2 y = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.393 |
|
|
\[
{}2 y^{\prime }+y = 3 t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.082 |
|
|
\[
{}\left (t -3\right ) y^{\prime }+\ln \left (t \right ) y = 2 t
\] |
[_linear] |
✓ |
3.266 |
|
|
\[
{}t \left (-4+t \right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
1.732 |
|
|
\[
{}y^{\prime }+\tan \left (t \right ) y = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.915 |
|
|
\[
{}\left (-t^{2}+4\right ) y^{\prime }+2 t y = 3 t^{2}
\] |
[_linear] |
✓ |
2.020 |
|
|
\[
{}\left (-t^{2}+4\right ) y^{\prime }+2 t y = 3 t^{2}
\] |
[_linear] |
✓ |
1.896 |
|
|
\[
{}\ln \left (t \right ) y^{\prime }+y = \cot \left (t \right )
\] |
[_linear] |
✓ |
3.000 |
|
|
\[
{}y^{\prime } = \frac {t -y}{2 t +5 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
8.684 |
|
|
\[
{}y^{\prime } = \sqrt {1-t^{2}-y^{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.691 |
|
|
\[
{}y^{\prime } = \frac {\ln \left (t y\right )}{1-t^{2}+y^{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
2.423 |
|
|
\[
{}y^{\prime } = \left (t^{2}+y^{2}\right )^{{3}/{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.540 |
|
|
\[
{}y^{\prime } = \frac {t^{2}+1}{3 y-y^{2}}
\] |
[_separable] |
✓ |
1.324 |
|
|
\[
{}y^{\prime } = \frac {\cot \left (t \right ) y}{y+1}
\] |
[_separable] |
✓ |
1.682 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
1.777 |
|
|
\[
{}y^{\prime } = -\frac {t}{2}+\frac {\sqrt {t^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.452 |
|
|
\[
{}y^{\prime } = -\frac {4 t}{y}
\] |
[_separable] |
✓ |
6.227 |
|
|
\[
{}y^{\prime } = 2 t y^{2}
\] |
[_separable] |
✓ |
2.020 |
|
|
\[
{}y^{\prime }+y^{3} = 0
\] |
[_quadrature] |
✓ |
1.700 |
|
|
\[
{}y^{\prime } = \frac {t^{2}}{y \left (t^{3}+1\right )}
\] |
[_separable] |
✓ |
2.132 |
|
|
\[
{}y^{\prime } = t y \left (3-y\right )
\] |
[_separable] |
✓ |
1.991 |
|
|
\[
{}y^{\prime } = y \left (3-t y\right )
\] |
[_Bernoulli] |
✓ |
1.537 |
|
|
\[
{}y^{\prime } = -y \left (3-t y\right )
\] |
[_Bernoulli] |
✓ |
1.523 |
|
|
\[
{}y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.664 |
|
|
\[
{}y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 1 & 1<t \end {array}\right .\right ) y = 0
\] |
[_separable] |
✓ |
1.237 |
|
|
\[
{}2 x +3+\left (2 y-2\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.671 |
|
|
\[
{}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.469 |
|
|
\[
{}3 x^{2}-2 x y+2+\left (6 y^{2}-x^{2}+3\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.418 |
|
|
\[
{}2 x y^{2}+2 y+\left (2 x^{2} y+2 x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.738 |
|
|
\[
{}y^{\prime } = -\frac {4 x +2 y}{2 x +3 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.113 |
|
|
\[
{}y^{\prime } = -\frac {4 x -2 y}{2 x -3 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
9.693 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )-2 y \sin \left (x \right )+\left ({\mathrm e}^{x} \cos \left (y\right )+2 \cos \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
6.993 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime } = 0
\] |
[‘x=_G(y,y’)‘] |
✗ |
8.477 |
|
|
\[
{}y \,{\mathrm e}^{x y} \cos \left (2 x \right )-2 \,{\mathrm e}^{x y} \sin \left (2 x \right )+2 x +\left (x \,{\mathrm e}^{x y} \cos \left (2 x \right )-3\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
36.070 |
|
|
\[
{}\frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.453 |
|
|
\[
{}x \ln \left (y\right )+x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.084 |
|
|
\[
{}\frac {x}{\left (y^{2}+x^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (y^{2}+x^{2}\right )^{{3}/{2}}} = 0
\] |
[_separable] |
✓ |
4.677 |
|
|
\[
{}2 x -y+\left (2 y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.932 |
|
|
\[
{}9 x^{2}+y-1-\left (4 y-x \right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.954 |
|
|
\[
{}y^{3} x^{2}+x \left (1+y^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.615 |
|
|
\[
{}\frac {\sin \left (y\right )}{y}-2 \,{\mathrm e}^{-x} \sin \left (x \right )+\frac {\left (\cos \left (y\right )+2 \,{\mathrm e}^{-x} \cos \left (x \right )\right ) y^{\prime }}{y} = 0
\] |
unknown |
✓ |
12.865 |
|
|
\[
{}y+\left (2 x -y \,{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
unknown |
✓ |
1.266 |
|
|
\[
{}\left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.206 |
|
|
\[
{}3 x^{2} y+2 x y+y^{3}+\left (y^{2}+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational] |
✓ |
2.147 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 x}+y-1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.097 |
|
|
\[
{}\frac {y^{\prime }}{\frac {x}{y}-\sin \left (y\right )} = 0
\] |
[_quadrature] |
✓ |
0.431 |
|
|
\[
{}y+\left (2 x y-{\mathrm e}^{-2 y}\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
1.742 |
|
|
\[
{}{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 y \csc \left (y\right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
3.644 |
|
|
\[
{}\frac {4 x^{3}}{y^{2}}+\frac {12}{y}+3 \left (\frac {x}{y^{2}}+4 y\right ) y^{\prime } = 0
\] |
[_rational] |
✗ |
1.344 |
|
|
\[
{}3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.489 |
|
|
\[
{}3 x y+y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.808 |
|
|
\[
{}y^{\prime } y = x +1
\] |
[_separable] |
✓ |
2.228 |
|
|
\[
{}\left (y^{4}+1\right ) y^{\prime } = x^{4}+1
\] |
[_separable] |
✓ |
1.291 |
|
|
\[
{}\frac {\left (3 x^{3}-x y^{2}\right ) y^{\prime }}{3 x^{2} y+y^{3}} = 1
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
32.068 |
|
|
\[
{}x \left (x -1\right ) y^{\prime } = y \left (y+1\right )
\] |
[_separable] |
✓ |
2.110 |
|