|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} y^{\prime }+2 x y = \sinh \left (x \right )
\] |
[_linear] |
✓ |
1.731 |
|
|
\[
{}y^{\prime }+\frac {y}{1-x}+2 x -x^{2} = 0
\] |
[_linear] |
✓ |
1.383 |
|
|
\[
{}y^{\prime }+\frac {y}{1-x}+x -x^{2} = 0
\] |
[_linear] |
✓ |
1.321 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1+x y
\] |
[_linear] |
✓ |
2.589 |
|
|
\[
{}y^{\prime }+x y = x y^{2}
\] |
[_separable] |
✓ |
2.364 |
|
|
\[
{}3 x y^{\prime }+y+x^{2} y^{4} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.141 |
|
|
\[
{}x \left (x +1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (-1+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.828 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-2 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.999 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.837 |
|
|
\[
{}x y^{\prime \prime }+\frac {y^{\prime }}{2}+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.345 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.990 |
|
|
\[
{}2 x y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.102 |
|
|
\[
{}x y^{\prime \prime }+x y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.017 |
|
|
\[
{}x \left (-1+x \right )^{2} y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.793 |
|
|
\[
{}y^{\prime }-\frac {2 y}{x}-x^{2} = 0
\] |
[_linear] |
✓ |
1.868 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x}-x^{3} = 0
\] |
[_linear] |
✓ |
1.648 |
|
|
\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+m y = 0
\] |
[_Laguerre] |
✗ |
0.702 |
|
|
\[
{}x y^{\prime } = x^{2}+2 x -3
\] |
[_quadrature] |
✓ |
0.574 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
2.413 |
|
|
\[
{}y^{\prime }+2 y = {\mathrm e}^{3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.398 |
|
|
\[
{}-y+x y^{\prime } = x^{2}
\] |
[_linear] |
✓ |
1.609 |
|
|
\[
{}x^{2} y^{\prime } = x^{3} \sin \left (3 x \right )+4
\] |
[_quadrature] |
✓ |
0.718 |
|
|
\[
{}x \cos \left (y\right ) y^{\prime }-\sin \left (y\right ) = 0
\] |
[_separable] |
✓ |
4.815 |
|
|
\[
{}\left (x^{3}+x y^{2}\right ) y^{\prime } = 2 y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
81.730 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
1.745 |
|
|
\[
{}y^{\prime }+y \tanh \left (x \right ) = 2 \sinh \left (x \right )
\] |
[_linear] |
✓ |
2.021 |
|
|
\[
{}x y^{\prime }-2 y = x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
1.865 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.724 |
|
|
\[
{}x y^{\prime }+3 y = y^{2} x^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.927 |
|
|
\[
{}x \left (y-3\right ) y^{\prime } = 4 y
\] |
[_separable] |
✓ |
2.255 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime } = x^{2} y
\] |
[_separable] |
✓ |
2.500 |
|
|
\[
{}x^{3}+\left (y+1\right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.896 |
|
|
\[
{}\cos \left (y\right )+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.280 |
|
|
\[
{}x^{2} \left (y+1\right )+y^{2} \left (-1+x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.714 |
|
|
\[
{}\left (2 y-x \right ) y^{\prime } = y+2 x
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.258 |
|
|
\[
{}x y+y^{2}+\left (x^{2}-x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
90.108 |
|
|
\[
{}x^{3}+y^{3} = 3 x y^{2} y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
11.470 |
|
|
\[
{}y-3 x +\left (4 y+3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
34.647 |
|
|
\[
{}\left (x^{3}+3 x y^{2}\right ) y^{\prime } = y^{3}+3 x^{2} y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
48.929 |
|
|
\[
{}-y+x y^{\prime } = x^{3}+3 x^{2}-2 x
\] |
[_linear] |
✓ |
0.240 |
|
|
\[
{}y^{\prime }+y \tan \left (x \right ) = \sin \left (x \right )
\] |
[_linear] |
✓ |
0.307 |
|
|
\[
{}-y+x y^{\prime } = x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
0.507 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+3 x y = 5 x
\] |
[_separable] |
✓ |
0.763 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = 5 \,{\mathrm e}^{\cos \left (x \right )}
\] |
[_linear] |
✓ |
0.526 |
|
|
\[
{}\left (3 x +3 y-4\right ) y^{\prime } = -x -y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.842 |
|
|
\[
{}x -x y^{2} = \left (x +x^{2} y\right ) y^{\prime }
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.569 |
|
|
\[
{}x -y-1+\left (4 y+x -1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
37.043 |
|
|
\[
{}3 y-7 x +7+\left (3-3 x +7 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.501 |
|
|
\[
{}y \left (1+x y\right )+x \left (1+x y+y^{2} x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.961 |
|
|
\[
{}y^{\prime }+y = x y^{3}
\] |
[_Bernoulli] |
✓ |
0.625 |
|
|
\[
{}y^{\prime }+y = y^{4} {\mathrm e}^{x}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
0.444 |
|
|
\[
{}2 y^{\prime }+y = y^{3} \left (-1+x \right )
\] |
[_Bernoulli] |
✓ |
0.695 |
|
|
\[
{}y^{\prime }-2 y \tan \left (x \right ) = y^{2} \tan \left (x \right )^{2}
\] |
[_Bernoulli] |
✓ |
0.527 |
|
|
\[
{}y^{\prime }+y \tan \left (x \right ) = y^{3} \sec \left (x \right )^{4}
\] |
[_Bernoulli] |
✓ |
0.583 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 1+x y
\] |
[_linear] |
✓ |
1.323 |
|
|
\[
{}x y y^{\prime }-\left (x +1\right ) \sqrt {y-1} = 0
\] |
[_separable] |
✓ |
1.898 |
|
|
\[
{}x^{2}-2 x y+5 y^{2} = \left (x^{2}+2 x y+y^{2}\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.169 |
|
|
\[
{}y^{\prime }-y \cot \left (x \right ) = y^{2} \sec \left (x \right )^{2}
\] |
[_Bernoulli] |
✓ |
2.944 |
|
|
\[
{}y+\left (x^{2}-4 x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.683 |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = \cos \left (x \right )-2 x \sin \left (x \right )
\] |
[_linear] |
✓ |
2.829 |
|
|
\[
{}y^{\prime } = \frac {2 x y+y^{2}}{x^{2}+2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
149.484 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (y+1\right )
\] |
[_separable] |
✓ |
1.562 |
|
|
\[
{}x y^{\prime }+2 y = 3 x -1
\] |
[_linear] |
✓ |
2.378 |
|
|
\[
{}x^{2} y^{\prime } = y^{2}-x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
49.591 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-2 y+3 x}
\] |
[_separable] |
✓ |
5.283 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
2.131 |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
7.364 |
|
|
\[
{}2 x y y^{\prime } = x^{2}-y^{2}
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
68.430 |
|
|
\[
{}y^{\prime } = \frac {x -2 y+1}{2 x -4 y}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.345 |
|
|
\[
{}\left (-x^{3}+1\right ) y^{\prime }+x^{2} y = x^{2} \left (-x^{3}+1\right )
\] |
[_linear] |
✓ |
2.940 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \sin \left (x \right )
\] |
[_linear] |
✓ |
1.757 |
|
|
\[
{}y^{\prime }+x +x y^{2} = 0
\] |
[_separable] |
✓ |
2.692 |
|
|
\[
{}y^{\prime }+\left (\frac {1}{x}-\frac {2 x}{-x^{2}+1}\right ) y = \frac {1}{-x^{2}+1}
\] |
[_linear] |
✓ |
1.392 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y = \left (x^{2}+1\right )^{{3}/{2}}
\] |
[_linear] |
✓ |
1.850 |
|
|
\[
{}x \left (1+y^{2}\right )-y \left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
4.468 |
|
|
\[
{}\frac {r \tan \left (\theta \right ) r^{\prime }}{a^{2}-r^{2}} = 1
\] |
[_separable] |
✓ |
2.770 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = \cos \left (x \right )
\] |
[_linear] |
✓ |
2.198 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = x y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.076 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 8
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.965 |
|
|
\[
{}y^{\prime \prime }-4 y = 10 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.242 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.089 |
|
|
\[
{}y^{\prime \prime }+25 y = 5 x^{2}+x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.383 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 4 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.395 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 2 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.527 |
|
|
\[
{}3 y^{\prime \prime }-2 y^{\prime }-y = 2 x -3
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.141 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+8 y = 8 \,{\mathrm e}^{4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.115 |
|
|
\[
{}2 y^{\prime \prime }-7 y^{\prime }-4 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.123 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 54 x +18
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.218 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 100 \sin \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.438 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 4 \sinh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.548 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 2 \cosh \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.200 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+10 y = 20-{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
22.611 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 2 \cos \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.832 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = x +{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.212 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+3 y = x^{2}-1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
20.257 |
|
|
\[
{}y^{\prime \prime }-9 y = {\mathrm e}^{3 x}+\sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.052 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+3 x = {\mathrm e}^{-3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.204 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 6 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
13.601 |
|
|
\[
{}x^{\prime \prime }-3 x^{\prime }+2 x = \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.329 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 3 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.800 |
|