|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} y^{\prime }+2 x y = \sinh \left (x \right )
\] |
[_linear] |
✓ |
1.700 |
|
|
\[
{}y^{\prime }+\frac {y}{1-x}+2 x -x^{2} = 0
\] |
[_linear] |
✓ |
1.319 |
|
|
\[
{}y^{\prime }+\frac {y}{1-x}+x -x^{2} = 0
\] |
[_linear] |
✓ |
1.230 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1+x y
\] |
[_linear] |
✓ |
2.473 |
|
|
\[
{}y^{\prime }+x y = x y^{2}
\] |
[_separable] |
✓ |
2.155 |
|
|
\[
{}3 y^{\prime } x +y+x^{2} y^{4} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.115 |
|
|
\[
{}x \left (x +1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.935 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-2 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.210 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.037 |
|
|
\[
{}x y^{\prime \prime }+\frac {y^{\prime }}{2}+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.469 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.229 |
|
|
\[
{}2 x y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.227 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.289 |
|
|
\[
{}x \left (x -1\right )^{2} y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.971 |
|
|
\[
{}y^{\prime }-\frac {2 y}{x}-x^{2} = 0
\] |
[_linear] |
✓ |
1.608 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x}-x^{3} = 0
\] |
[_linear] |
✓ |
1.656 |
|
|
\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+m y = 0
\] |
[_Laguerre] |
✗ |
0.799 |
|
|
\[
{}y^{\prime } x = x^{2}+2 x -3
\] |
[_quadrature] |
✓ |
0.543 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
2.308 |
|
|
\[
{}y^{\prime }+2 y = {\mathrm e}^{3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.317 |
|
|
\[
{}-y+y^{\prime } x = x^{2}
\] |
[_linear] |
✓ |
1.596 |
|
|
\[
{}x^{2} y^{\prime } = x^{3} \sin \left (3 x \right )+4
\] |
[_quadrature] |
✓ |
0.730 |
|
|
\[
{}x \cos \left (y\right ) y^{\prime }-\sin \left (y\right ) = 0
\] |
[_separable] |
✓ |
4.072 |
|
|
\[
{}\left (x^{3}+x y^{2}\right ) y^{\prime } = 2 y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
74.761 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
1.600 |
|
|
\[
{}y^{\prime }+y \tanh \left (x \right ) = 2 \sinh \left (x \right )
\] |
[_linear] |
✓ |
1.909 |
|
|
\[
{}y^{\prime } x -2 y = x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
1.843 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.993 |
|
|
\[
{}y^{\prime } x +3 y = x^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.799 |
|
|
\[
{}x \left (y-3\right ) y^{\prime } = 4 y
\] |
[_separable] |
✓ |
2.101 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime } = x^{2} y
\] |
[_separable] |
✓ |
2.674 |
|
|
\[
{}x^{3}+\left (1+y\right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.884 |
|
|
\[
{}\cos \left (y\right )+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.997 |
|
|
\[
{}x^{2} \left (1+y\right )+y^{2} \left (x -1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.380 |
|
|
\[
{}\left (2 y-x \right ) y^{\prime } = y+2 x
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.401 |
|
|
\[
{}x y+y^{2}+\left (x^{2}-x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.889 |
|
|
\[
{}x^{3}+y^{3} = 3 x y^{2} y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
10.327 |
|
|
\[
{}y-3 x +\left (4 y+3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.831 |
|
|
\[
{}\left (x^{3}+3 x y^{2}\right ) y^{\prime } = y^{3}+3 x^{2} y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
47.529 |
|
|
\[
{}-y+y^{\prime } x = x^{3}+3 x^{2}-2 x
\] |
[_linear] |
✓ |
0.257 |
|
|
\[
{}y^{\prime }+y \tan \left (x \right ) = \sin \left (x \right )
\] |
[_linear] |
✓ |
0.323 |
|
|
\[
{}-y+y^{\prime } x = x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
0.463 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+3 x y = 5 x
\] |
[_separable] |
✓ |
0.706 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = 5 \,{\mathrm e}^{\cos \left (x \right )}
\] |
[_linear] |
✓ |
0.491 |
|
|
\[
{}\left (3 x +3 y-4\right ) y^{\prime } = -x -y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.783 |
|
|
\[
{}x -x y^{2} = \left (x +x^{2} y\right ) y^{\prime }
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.968 |
|
|
\[
{}x -y-1+\left (4 y+x -1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.511 |
|
|
\[
{}\left (3-3 x +7 y\right ) y^{\prime }+7-7 x +3 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.158 |
|
|
\[
{}y \left (1+x y\right )+x \left (1+x y+x^{2} y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.865 |
|
|
\[
{}y^{\prime }+y = x y^{3}
\] |
[_Bernoulli] |
✓ |
0.517 |
|
|
\[
{}y^{\prime }+y = y^{4} {\mathrm e}^{x}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
0.436 |
|
|
\[
{}2 y^{\prime }+y = y^{3} \left (x -1\right )
\] |
[_Bernoulli] |
✓ |
0.510 |
|
|
\[
{}y^{\prime }-2 y \tan \left (x \right ) = y^{2} \tan \left (x \right )^{2}
\] |
[_Bernoulli] |
✓ |
0.443 |
|
|
\[
{}y^{\prime }+y \tan \left (x \right ) = y^{3} \sec \left (x \right )^{4}
\] |
[_Bernoulli] |
✓ |
0.532 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 1+x y
\] |
[_linear] |
✓ |
1.298 |
|
|
\[
{}x y y^{\prime }-\left (x +1\right ) \sqrt {-1+y} = 0
\] |
[_separable] |
✓ |
1.714 |
|
|
\[
{}x^{2}-2 x y+5 y^{2} = \left (x^{2}+2 x y+y^{2}\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.706 |
|
|
\[
{}y^{\prime }-y \cot \left (x \right ) = y^{2} \sec \left (x \right )^{2}
\] |
[_Bernoulli] |
✓ |
2.778 |
|
|
\[
{}y+\left (x^{2}-4 x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.762 |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = \cos \left (x \right )-2 x \sin \left (x \right )
\] |
[_linear] |
✓ |
2.744 |
|
|
\[
{}y^{\prime } = \frac {2 x y+y^{2}}{x^{2}+2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
73.857 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (1+y\right )
\] |
[_separable] |
✓ |
1.615 |
|
|
\[
{}y^{\prime } x +2 y = 3 x -1
\] |
[_linear] |
✓ |
2.252 |
|
|
\[
{}x^{2} y^{\prime } = y^{2}-x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
9.914 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3 x -2 y}
\] |
[_separable] |
✓ |
4.157 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
1.907 |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
19.190 |
|
|
\[
{}2 x y y^{\prime } = x^{2}-y^{2}
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
4.319 |
|
|
\[
{}y^{\prime } = \frac {x -2 y+1}{2 x -4 y}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.727 |
|
|
\[
{}\left (-x^{3}+1\right ) y^{\prime }+x^{2} y = x^{2} \left (-x^{3}+1\right )
\] |
[_linear] |
✓ |
2.813 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \sin \left (x \right )
\] |
[_linear] |
✓ |
1.683 |
|
|
\[
{}y^{\prime }+x +x y^{2} = 0
\] |
[_separable] |
✓ |
2.849 |
|
|
\[
{}y^{\prime }+\left (\frac {1}{x}-\frac {2 x}{-x^{2}+1}\right ) y = \frac {1}{-x^{2}+1}
\] |
[_linear] |
✓ |
1.345 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y = \left (x^{2}+1\right )^{{3}/{2}}
\] |
[_linear] |
✓ |
1.816 |
|
|
\[
{}x \left (1+y^{2}\right )-y \left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.720 |
|
|
\[
{}\frac {r \tan \left (\theta \right ) r^{\prime }}{a^{2}-r^{2}} = 1
\] |
[_separable] |
✓ |
2.424 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = \cos \left (x \right )
\] |
[_linear] |
✓ |
2.149 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = x y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.977 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 8
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.271 |
|
|
\[
{}y^{\prime \prime }-4 y = 10 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.316 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.364 |
|
|
\[
{}y^{\prime \prime }+25 y = 5 x^{2}+x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.732 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 4 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.680 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 2 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.624 |
|
|
\[
{}3 y^{\prime \prime }-2 y^{\prime }-y = 2 x -3
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.342 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+8 y = 8 \,{\mathrm e}^{4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.352 |
|
|
\[
{}2 y^{\prime \prime }-7 y^{\prime }-4 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.328 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 54 x +18
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.411 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 100 \sin \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.736 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 4 \sinh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.830 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 2 \cosh \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.548 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+10 y = 20-{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
23.319 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 2 \cos \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.114 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = x +{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.427 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+3 y = x^{2}-1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
20.190 |
|
|
\[
{}y^{\prime \prime }-9 y = {\mathrm e}^{3 x}+\sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.112 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+3 x = {\mathrm e}^{-3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.958 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 6 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.268 |
|
|
\[
{}x^{\prime \prime }-3 x^{\prime }+2 x = \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.625 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 3 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.069 |
|