|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } x = 5 y+x +1
\] |
[_linear] |
✓ |
2.837 |
|
|
\[
{}x^{2} y^{\prime }+y-2 y x -2 x^{2} = 0
\] |
[_linear] |
✓ |
4.354 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+2 y = \frac {{\mathrm e}^{x}}{x +1}
\] |
[_linear] |
✓ |
1.648 |
|
|
\[
{}\cos \left (y\right )^{2}+\left (x -\tan \left (y\right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
5.473 |
|
|
\[
{}2 y = \left (y^{4}+x \right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
5.345 |
|
|
\[
{}\cos \left (\theta \right ) r^{\prime } = 2+2 r \sin \left (\theta \right )
\] |
[_linear] |
✓ |
4.961 |
|
|
\[
{}\sin \left (\theta \right ) r^{\prime }+1+r \tan \left (\theta \right ) = \cos \left (\theta \right )
\] |
[_linear] |
✓ |
7.725 |
|
|
\[
{}y x^{\prime } = 2 y \,{\mathrm e}^{3 y}+x \left (3 y +2\right )
\] |
[_linear] |
✓ |
5.010 |
|
|
\[
{}y^{2}+1+\left (2 y x -y^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.423 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right )-\sec \left (x \right ) = 0
\] |
[_linear] |
✓ |
1.738 |
|
|
\[
{}y+y^{3}+4 \left (x y^{2}-1\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
4.512 |
|
|
\[
{}2 y-y x -3+y^{\prime } x = 0
\] |
[_linear] |
✓ |
1.284 |
|
|
\[
{}y+2 \left (x -2 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
11.879 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+\left (x^{2}-1\right )^{2}+4 y = 0
\] |
[_linear] |
✓ |
1.451 |
|
|
\[
{}3 y^{2} y^{\prime }-x y^{3} = {\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right )
\] |
[_Bernoulli] |
✓ |
8.109 |
|
|
\[
{}y^{3} y^{\prime }+x y^{4} = x \,{\mathrm e}^{-x^{2}}
\] |
[_Bernoulli] |
✓ |
9.152 |
|
|
\[
{}\cosh \left (y\right ) y^{\prime }+\sinh \left (y\right )-{\mathrm e}^{-x} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.548 |
|
|
\[
{}\sin \left (\theta \right ) \theta ^{\prime }+\cos \left (\theta \right )-t \,{\mathrm e}^{-t} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
3.041 |
|
|
\[
{}x y y^{\prime } = x^{2}-y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
22.375 |
|
|
\[
{}y^{\prime }-y x = \sqrt {y}\, x \,{\mathrm e}^{x^{2}}
\] |
[_Bernoulli] |
✓ |
2.179 |
|
|
\[
{}t x^{\prime }+x \left (1-x^{2} t^{4}\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
8.909 |
|
|
\[
{}x^{2} y^{\prime }+y^{2} = y x
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.896 |
|
|
\[
{}\csc \left (y\right ) \cot \left (y\right ) y^{\prime } = \csc \left (y\right )+{\mathrm e}^{x}
\] |
[‘y=_G(x,y’)‘] |
✓ |
5.866 |
|
|
\[
{}y^{\prime }-y x = \frac {x}{y}
\] |
[_separable] |
✓ |
2.465 |
|
|
\[
{}y+y^{\prime } x = y^{2} x^{2} \cos \left (x \right )
\] |
[_Bernoulli] |
✓ |
7.847 |
|
|
\[
{}r^{\prime }+\left (r-\frac {1}{r}\right ) \theta = 0
\] |
[_separable] |
✓ |
2.428 |
|
|
\[
{}y^{\prime } x +2 y = 3 x^{3} y^{{4}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
22.669 |
|
|
\[
{}3 y^{\prime }+\frac {2 y}{x +1} = \frac {x}{y^{2}}
\] |
[_rational, _Bernoulli] |
✓ |
5.757 |
|
|
\[
{}\cos \left (y\right ) y^{\prime }+\left (\sin \left (y\right )-1\right ) \cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
88.289 |
|
|
\[
{}\left (x \tan \left (y\right )^{2}+x \right ) y^{\prime } = 2 x^{2}+\tan \left (y\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
4.744 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = y^{3} \sin \left (x \right )
\] |
[_Bernoulli] |
✓ |
3.620 |
|
|
\[
{}y^{\prime }+y = y^{2} {\mathrm e}^{-t}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
7.072 |
|
|
\[
{}y^{\prime } = x \left (1-{\mathrm e}^{2 y-x^{2}}\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
2.266 |
|
|
\[
{}2 y = \left (x^{2} y^{4}+x \right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
20.275 |
|
|
\[
{}1+x y \left (1+x y^{2}\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✗ |
0.883 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+y x = x \left (-x^{2}+1\right ) \sqrt {y}
\] |
[_rational, _Bernoulli] |
✗ |
5.136 |
|
|
\[
{}\left (1-x \right ) y^{\prime }-1-y = 0
\] |
[_separable] |
✓ |
2.354 |
|
|
\[
{}y^{2}+\left (y x +x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
35.062 |
|
|
\[
{}2 x +y-\left (x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.734 |
|
|
\[
{}x \ln \left (x \right ) y^{\prime }-x +y = 0
\] |
[_linear] |
✓ |
4.673 |
|
|
\[
{}x -2 y+1+\left (y-2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.261 |
|
|
\[
{}2 y x -2 x y^{3}+x^{3}+\left (x^{2}+y^{2}-3 x^{2} y^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
2.125 |
|
|
\[
{}2 \,{\mathrm e}^{x}-t^{2}+t \,{\mathrm e}^{x} x^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
5.759 |
|
|
\[
{}6+2 y = x y y^{\prime }
\] |
[_separable] |
✓ |
3.982 |
|
|
\[
{}x -3 y = \left (3 y-x +2\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.650 |
|
|
\[
{}y \sin \left (x \right )-2 \cos \left (y\right )+\tan \left (x \right )-\left (\cos \left (x \right )-2 x \sin \left (y\right )+\sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
99.072 |
|
|
\[
{}x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
31.405 |
|
|
\[
{}y-y^{\prime } x = 2 y^{2}+2 y^{\prime }
\] |
[_separable] |
✓ |
6.821 |
|
|
\[
{}\tan \left (y\right ) = \left (3 x +4\right ) y^{\prime }
\] |
[_separable] |
✓ |
7.433 |
|
|
\[
{}y^{\prime }+y \ln \left (y\right ) \tan \left (x \right ) = 2 y
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
3.259 |
|
|
\[
{}2 y x +y^{4}+\left (x y^{3}-2 x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
8.163 |
|
|
\[
{}y+\left (3 x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
47.447 |
|
|
\[
{}r^{\prime } = r \cot \left (\theta \right )
\] |
[_separable] |
✓ |
6.077 |
|
|
\[
{}\left (3 x +4 y\right ) y^{\prime }+y+2 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.768 |
|
|
\[
{}2 x^{3}-y^{3}-3 x +3 x y^{2} y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
2.631 |
|
|
\[
{}y^{\prime } x -y-\sqrt {x^{2}+y^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
21.318 |
|
|
\[
{}y^{\prime } = \cos \left (y\right ) \cos \left (x \right )^{2}
\] |
[_separable] |
✓ |
6.296 |
|
|
\[
{}x +y+\left (2 x +3 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
14.637 |
|
|
\[
{}1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
11.812 |
|
|
\[
{}y^{\prime }+x +y \cot \left (x \right ) = 0
\] |
[_linear] |
✓ |
1.471 |
|
|
\[
{}3 x -6 = x y y^{\prime }
\] |
[_separable] |
✓ |
4.818 |
|
|
\[
{}x -2 y x +{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.026 |
|
|
\[
{}2 y^{\prime } x -y+\frac {x^{2}}{y^{2}} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
12.227 |
|
|
\[
{}y^{\prime } x +y \left (1+y^{2}\right ) = 0
\] |
[_separable] |
✓ |
12.788 |
|
|
\[
{}y \sqrt {x^{2}+y^{2}}+y x = x^{2} y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
44.260 |
|
|
\[
{}3 \,{\mathrm e}^{x} \tan \left (y\right ) = \left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime }
\] |
[_separable] |
✓ |
7.752 |
|
|
\[
{}\sec \left (y\right )^{2} y^{\prime } = \tan \left (y\right )+2 x \,{\mathrm e}^{x}
\] |
[‘y=_G(x,y’)‘] |
✓ |
7.471 |
|
|
\[
{}2 x \tan \left (y\right )+3 y^{2}+x^{2}+\left (x^{2} \sec \left (y\right )^{2}+6 y x -y^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
107.572 |
|
|
\[
{}y \cos \left (\frac {x}{y}\right )-\left (y+x \cos \left (\frac {x}{y}\right )\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
19.819 |
|
|
\[
{}y \left (3 x^{2}+y\right )-x \left (x^{2}-y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
10.800 |
|
|
\[
{}x +\left (2 x +3 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
9.375 |
|
|
\[
{}y^{\prime } x -5 y-x \sqrt {y} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
22.917 |
|
|
\[
{}x \sqrt {1-y}-\sqrt {-x^{2}+1}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
3.606 |
|
|
\[
{}y x -y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.146 |
|
|
\[
{}x \,{\mathrm e}^{-y^{2}}+y y^{\prime } = 0
\] |
[_separable] |
✓ |
2.124 |
|
|
\[
{}\frac {2 y^{3}-2 x^{2} y^{3}-x +x y^{2} \ln \left (y\right )}{x y^{2}}+\frac {\left (2 y^{3} \ln \left (x \right )-x^{2} y^{3}+2 x +x y^{2}\right ) y^{\prime }}{y^{3}} = 0
\] |
[_exact] |
✓ |
20.364 |
|
|
\[
{}y^{\prime } x -2 y-2 x^{4} y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
15.267 |
|
|
\[
{}\left (-2 x^{2}-3 y x \right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
20.909 |
|
|
\[
{}y^{\prime } x = x^{4}+4 y
\] |
[_linear] |
✓ |
1.565 |
|
|
\[
{}y+y^{\prime } x = x^{3} y^{6}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
20.298 |
|
|
\[
{}x^{\prime } = x+x^{2} {\mathrm e}^{\theta }
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
7.383 |
|
|
\[
{}x^{2}+y^{2} = 2 x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
41.307 |
|
|
\[
{}3 y x +\left (3 x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
130.062 |
|
|
\[
{}y^{\prime }+2 y = 3 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.714 |
|
|
\[
{}4 x y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.806 |
|
|
\[
{}x -2 y+3 = \left (x -2 y+1\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.997 |
|
|
\[
{}y^{2}+\left (x^{3}-2 y x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
45.913 |
|
|
\[
{}2 y x -2 y+1+x \left (x -1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.725 |
|
|
\[
{}y^{3}+2 x^{2} y+\left (-3 x^{3}-2 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
376.298 |
|
|
\[
{}2 \left (x^{2}+1\right ) y^{\prime } = \left (2 y^{2}-1\right ) x y
\] |
[_separable] |
✓ |
12.832 |
|
|
\[
{}y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
0.694 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
7.537 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.510 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.450 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.458 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.470 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.883 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.869 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.897 |
|
|
\[
{}2 y^{\prime \prime }+2 y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.866 |
|