|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } x +y = y^{2} \ln \left (x \right )
\] |
[_Bernoulli] |
✓ |
2.106 |
|
|
\[
{}x^{\prime }+2 x y = {\mathrm e}^{-y^{2}}
\] |
[_linear] |
✓ |
1.263 |
|
|
\[
{}r^{\prime } = \left (r+{\mathrm e}^{-\theta }\right ) \tan \left (\theta \right )
\] |
[_linear] |
✓ |
1.652 |
|
|
\[
{}y^{\prime }-\frac {2 x y}{x^{2}+1} = 1
\] |
[_linear] |
✓ |
1.333 |
|
|
\[
{}y^{\prime }+y = x y^{3}
\] |
[_Bernoulli] |
✓ |
0.373 |
|
|
\[
{}\left (-x^{3}+1\right ) y^{\prime }-2 \left (x +1\right ) y = y^{{5}/{2}}
\] |
[_rational, _Bernoulli] |
✓ |
4.762 |
|
|
\[
{}\tan \left (\theta \right ) r^{\prime }-r = \tan \left (\theta \right )^{2}
\] |
[_linear] |
✓ |
1.463 |
|
|
\[
{}y^{\prime }+2 y = 3 \,{\mathrm e}^{-2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.898 |
|
|
\[
{}y^{\prime }+2 y = \frac {3 \,{\mathrm e}^{-2 x}}{4}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.940 |
|
|
\[
{}y^{\prime }+2 y = \sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.124 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = {\mathrm e}^{2 x}
\] |
[_linear] |
✓ |
1.877 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2}
\] |
[_linear] |
✓ |
2.390 |
|
|
\[
{}y^{\prime } x +y = x \sin \left (x \right )
\] |
[_linear] |
✓ |
1.157 |
|
|
\[
{}-y+y^{\prime } x = x^{2} \sin \left (x \right )
\] |
[_linear] |
✓ |
1.173 |
|
|
\[
{}y^{\prime } x +x y^{2}-y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
1.707 |
|
|
\[
{}y^{\prime } x -y \left (2 y \ln \left (x \right )-1\right ) = 0
\] |
[_Bernoulli] |
✓ |
2.202 |
|
|
\[
{}x^{2} \left (x -1\right ) y^{\prime }-y^{2}-x \left (x -2\right ) y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.050 |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.058 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \frac {y^{2}}{x}
\] |
[_separable] |
✓ |
3.168 |
|
|
\[
{}2 \cos \left (x \right ) y^{\prime } = y \sin \left (x \right )-y^{3}
\] |
[_Bernoulli] |
✓ |
7.331 |
|
|
\[
{}\left (x -\cos \left (y\right )\right ) y^{\prime }+\tan \left (y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
4.931 |
|
|
\[
{}y^{\prime } = x^{3}+\frac {2 y}{x}-\frac {y^{2}}{x}
\] |
[_rational, _Riccati] |
✓ |
1.386 |
|
|
\[
{}y^{\prime } = 2 \tan \left (x \right ) \sec \left (x \right )-y^{2} \sin \left (x \right )
\] |
[_Riccati] |
✓ |
3.979 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}}-\frac {y}{x}-y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.616 |
|
|
\[
{}y^{\prime } = 1+\frac {y}{x}-\frac {y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.071 |
|
|
\[
{}2 x y y^{\prime }+\left (x +1\right ) y^{2} = {\mathrm e}^{x}
\] |
[_Bernoulli] |
✓ |
1.662 |
|
|
\[
{}\cos \left (y\right ) y^{\prime }+\sin \left (y\right ) = x^{2}
\] |
[‘y=_G(x,y’)‘] |
✓ |
1.965 |
|
|
\[
{}\left (x +1\right ) y^{\prime }-1-y = \left (x +1\right ) \sqrt {1+y}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.682 |
|
|
\[
{}{\mathrm e}^{y} \left (1+y^{\prime }\right ) = {\mathrm e}^{x}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.311 |
|
|
\[
{}y^{\prime } \sin \left (y\right )+\sin \left (x \right ) \cos \left (y\right ) = \sin \left (x \right )
\] |
[_separable] |
✓ |
75.284 |
|
|
\[
{}\left (x -y\right )^{2} y^{\prime } = 4
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.257 |
|
|
\[
{}-y+y^{\prime } x = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.762 |
|
|
\[
{}\left (3 x +2 y+1\right ) y^{\prime }+4 x +3 y+2 = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.444 |
|
|
\[
{}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 y x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.082 |
|
|
\[
{}y+\left (1+y^{2} {\mathrm e}^{2 x}\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.157 |
|
|
\[
{}x^{2} y+y^{2}+x^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.692 |
|
|
\[
{}y^{2} {\mathrm e}^{x y^{2}}+4 x^{3}+\left (2 x y \,{\mathrm e}^{x y^{2}}-3 y^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
68.445 |
|
|
\[
{}y^{\prime } = \left (x^{2}+2 y-1\right )^{{2}/{3}}-x
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.263 |
|
|
\[
{}y^{\prime } x +y = x^{2} \left (1+{\mathrm e}^{x}\right ) y^{2}
\] |
[_Bernoulli] |
✓ |
2.797 |
|
|
\[
{}2 y-x y \ln \left (x \right )-2 y^{\prime } x \ln \left (x \right ) = 0
\] |
[_separable] |
✓ |
1.597 |
|
|
\[
{}y^{\prime }+a y = k \,{\mathrm e}^{b x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.894 |
|
|
\[
{}y^{\prime } = \left (x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.363 |
|
|
\[
{}y^{\prime }+8 x^{3} y^{3}+2 y x = 0
\] |
[_Bernoulli] |
✓ |
1.095 |
|
|
\[
{}\left (x y \sqrt {x^{2}-y^{2}}+x \right ) y^{\prime } = y-x^{2} \sqrt {x^{2}-y^{2}}
\] |
[NONE] |
✗ |
2.787 |
|
|
\[
{}y^{\prime }+a y = b \sin \left (k x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.165 |
|
|
\[
{}y^{\prime } x -y^{2}+1 = 0
\] |
[_separable] |
✓ |
1.288 |
|
|
\[
{}\left (y^{2}+a \sin \left (x \right )\right ) y^{\prime } = \cos \left (x \right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.857 |
|
|
\[
{}y^{\prime } x = x \,{\mathrm e}^{\frac {y}{x}}+x +y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
9.315 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = {\mathrm e}^{-\sin \left (x \right )}
\] |
[_linear] |
✓ |
1.452 |
|
|
\[
{}y^{\prime } x -y \left (\ln \left (y x \right )-1\right ) = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.669 |
|
|
\[
{}x^{3} y^{\prime }-y^{2}-x^{2} y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
1.762 |
|
|
\[
{}y^{\prime } x +a y+b \,x^{n} = 0
\] |
[_linear] |
✓ |
1.000 |
|
|
\[
{}y^{\prime } x -y-x \sin \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
2.977 |
|
|
\[
{}y^{2}-3 y x -2 x^{2}+\left (y x -x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.214 |
|
|
\[
{}\left (6 y x +x^{2}+3\right ) y^{\prime }+3 y^{2}+2 y x +2 x = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.328 |
|
|
\[
{}x^{2} y^{\prime }+y^{2}+y x +x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
1.570 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 y x -\cos \left (x \right ) = 0
\] |
[_linear] |
✓ |
2.597 |
|
|
\[
{}\left (x^{2} y-1\right ) y^{\prime }+x y^{2}-1 = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.206 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+y x -3 x y^{2} = 0
\] |
[_separable] |
✓ |
2.546 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right ) = 0
\] |
[_separable] |
✓ |
2.368 |
|
|
\[
{}\left (1+x^{2}+y^{2}\right ) y^{\prime }+2 y x +x^{2}+3 = 0
\] |
[_exact, _rational] |
✓ |
1.216 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+y+\left (1+\sin \left (x \right )\right ) \cos \left (x \right ) = 0
\] |
[_linear] |
✓ |
2.825 |
|
|
\[
{}y^{2}+12 x^{2} y+\left (2 y x +4 x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.647 |
|
|
\[
{}\left (x^{2}-y\right ) y^{\prime }+x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
0.865 |
|
|
\[
{}\left (x^{2}-y\right ) y^{\prime }-4 y x = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.876 |
|
|
\[
{}x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.325 |
|
|
\[
{}2 x y y^{\prime }+3 x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
59.954 |
|
|
\[
{}\left (2 x y^{3}-x^{4}\right ) y^{\prime }+2 x^{3} y-y^{4} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.802 |
|
|
\[
{}\left (y x -1\right )^{2} x y^{\prime }+\left (1+x^{2} y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.753 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (y+2 x \right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
4.056 |
|
|
\[
{}3 x y^{2} y^{\prime }+y^{3}-2 x = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
2.096 |
|
|
\[
{}2 y^{3} y^{\prime }+x y^{2}-x^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
15.948 |
|
|
\[
{}\left (2 x y^{3}+y x +x^{2}\right ) y^{\prime }-y x +y^{2} = 0
\] |
[_rational] |
✓ |
1.511 |
|
|
\[
{}\left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x = 0
\] |
[_separable] |
✓ |
1.805 |
|
|
\[
{}y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x} = 0
\] |
[_separable] |
✓ |
1.310 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.428 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.766 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.839 |
|
|
\[
{}6 y^{\prime \prime }-11 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.782 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.990 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }-6 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-4 y^{\prime \prime }+4 y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.066 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-2 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\prime \prime \prime \prime }-a^{2} y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.089 |
|
|
\[
{}y^{\prime \prime }-2 k y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.974 |
|
|
\[
{}y^{\prime \prime }+4 k y^{\prime }-12 k^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.827 |
|
|
\[
{}y^{\prime \prime \prime \prime } = 0
\] |
[[_high_order, _quadrature]] |
✓ |
0.037 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.774 |
|
|
\[
{}3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.065 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.067 |
|
|
\[
{}y^{\prime \prime }-2 a y^{\prime }+a^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.622 |
|
|
\[
{}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.062 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-11 y^{\prime \prime }-12 y^{\prime }+36 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.076 |
|
|
\[
{}36 y^{\prime \prime \prime \prime }-37 y^{\prime \prime }+4 y^{\prime }+5 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+36 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.127 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.421 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.576 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+6 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.077 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+20 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.463 |
|