|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = 3-\sin \left (y\right )
\] |
[_quadrature] |
✓ |
37.606 |
|
|
\[
{}y^{\prime }+4 y = {\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.427 |
|
|
\[
{}x y^{\prime } = \arcsin \left (x^{2}\right )
\] |
[_quadrature] |
✓ |
43.776 |
|
|
\[
{}y y^{\prime } = 2 x
\] |
[_separable] |
✓ |
4.183 |
|
|
\[
{}y^{\prime \prime } = \frac {x +1}{-1+x}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.980 |
|
|
\[
{}x^{2} y^{\prime \prime } = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.480 |
|
|
\[
{}y^{2} y^{\prime \prime } = 8 x^{2}
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.116 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+8 y = {\mathrm e}^{-x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
27.324 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.548 |
|
|
\[
{}y^{\prime } = 4 x^{3}
\] |
[_quadrature] |
✓ |
0.454 |
|
|
\[
{}y^{\prime } = 20 \,{\mathrm e}^{-4 x}
\] |
[_quadrature] |
✓ |
0.541 |
|
|
\[
{}x y^{\prime }+\sqrt {x} = 2
\] |
[_quadrature] |
✓ |
0.509 |
|
|
\[
{}\sqrt {x +4}\, y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.606 |
|
|
\[
{}y^{\prime } = x \cos \left (x^{2}\right )
\] |
[_quadrature] |
✓ |
0.590 |
|
|
\[
{}y^{\prime } = x \cos \left (x \right )
\] |
[_quadrature] |
✓ |
0.520 |
|
|
\[
{}x = \left (x^{2}-9\right ) y^{\prime }
\] |
[_quadrature] |
✓ |
0.624 |
|
|
\[
{}1 = \left (x^{2}-9\right ) y^{\prime }
\] |
[_quadrature] |
✓ |
0.648 |
|
|
\[
{}1 = x^{2}-9 y^{\prime }
\] |
[_quadrature] |
✓ |
0.460 |
|
|
\[
{}y^{\prime \prime } = \sin \left (2 x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.169 |
|
|
\[
{}y^{\prime \prime }-3 = x
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.877 |
|
|
\[
{}y^{\prime \prime \prime \prime } = 1
\] |
[[_high_order, _quadrature]] |
✓ |
0.090 |
|
|
\[
{}y^{\prime } = 40 x \,{\mathrm e}^{2 x}
\] |
[_quadrature] |
✓ |
0.769 |
|
|
\[
{}\left (x +6\right )^{{1}/{3}} y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.682 |
|
|
\[
{}y^{\prime } = \frac {-1+x}{x +1}
\] |
[_quadrature] |
✓ |
0.767 |
|
|
\[
{}x y^{\prime }+2 = \sqrt {x}
\] |
[_quadrature] |
✓ |
0.836 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }-\sin \left (x \right ) = 0
\] |
[_quadrature] |
✓ |
2.224 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.805 |
|
|
\[
{}x y^{\prime \prime }+2 = \sqrt {x}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.563 |
|
|
\[
{}y^{\prime } = \sin \left (\frac {x}{2}\right )
\] |
[_quadrature] |
✓ |
0.612 |
|
|
\[
{}y^{\prime } = \sin \left (\frac {x}{2}\right )
\] |
[_quadrature] |
✓ |
0.763 |
|
|
\[
{}y^{\prime } = \sin \left (\frac {x}{2}\right )
\] |
[_quadrature] |
✓ |
0.791 |
|
|
\[
{}y^{\prime } = 3 \sqrt {x +3}
\] |
[_quadrature] |
✓ |
0.563 |
|
|
\[
{}y^{\prime } = 3 \sqrt {x +3}
\] |
[_quadrature] |
✓ |
0.537 |
|
|
\[
{}y^{\prime } = 3 \sqrt {x +3}
\] |
[_quadrature] |
✓ |
0.520 |
|
|
\[
{}y^{\prime } = 3 \sqrt {x +3}
\] |
[_quadrature] |
✓ |
0.514 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{-x^{2}}
\] |
[_quadrature] |
✓ |
0.736 |
|
|
\[
{}y^{\prime } = \frac {x}{\sqrt {x^{2}+5}}
\] |
[_quadrature] |
✓ |
1.146 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}+1}
\] |
[_quadrature] |
✓ |
0.769 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-9 x^{2}}
\] |
[_quadrature] |
✓ |
0.606 |
|
|
\[
{}x y^{\prime } = \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.881 |
|
|
\[
{}x y^{\prime } = \sin \left (x^{2}\right )
\] |
[_quadrature] |
✓ |
0.929 |
|
|
\[
{}y^{\prime } = \left \{\begin {array}{cc} 0 & x <0 \\ 1 & 0\le x \end {array}\right .
\] |
[_quadrature] |
✓ |
0.478 |
|
|
\[
{}y^{\prime } = \left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x \end {array}\right .
\] |
[_quadrature] |
✓ |
0.494 |
|
|
\[
{}y^{\prime } = \left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x <2 \\ 0 & 2\le x \end {array}\right .
\] |
[_quadrature] |
✓ |
0.528 |
|
|
\[
{}y^{\prime }+3 x y = 6 x
\] |
[_separable] |
✓ |
1.564 |
|
|
\[
{}\sin \left (x +y\right )-y y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
12.661 |
|
|
\[
{}y^{\prime }-y^{3} = 8
\] |
[_quadrature] |
✓ |
82.019 |
|
|
\[
{}x^{2} y^{\prime }+x y^{2} = x
\] |
[_separable] |
✓ |
1.944 |
|
|
\[
{}y^{\prime }-y^{2} = x
\] |
[[_Riccati, _special]] |
✓ |
1.077 |
|
|
\[
{}y^{3}-25 y+y^{\prime } = 0
\] |
[_quadrature] |
✓ |
3.625 |
|
|
\[
{}\left (-2+x \right ) y^{\prime } = 3+y
\] |
[_separable] |
✓ |
2.083 |
|
|
\[
{}\left (y-2\right ) y^{\prime } = x -3
\] |
[_separable] |
✓ |
3.553 |
|
|
\[
{}y^{\prime }+2 y-y^{2} = -2
\] |
[_quadrature] |
✓ |
1.342 |
|
|
\[
{}y^{\prime }+\left (8-x \right ) y-y^{2} = -8 x
\] |
[_Riccati] |
✓ |
1.655 |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
1.690 |
|
|
\[
{}y^{\prime } = 3 y^{2}-y^{2} \sin \left (x \right )
\] |
[_separable] |
✓ |
2.406 |
|
|
\[
{}y^{\prime } = 3 x -y \sin \left (x \right )
\] |
[_linear] |
✓ |
1.858 |
|
|
\[
{}x y^{\prime } = \left (x -y\right )^{2}
\] |
[_rational, _Riccati] |
✓ |
1.960 |
|
|
\[
{}y^{\prime } = \sqrt {x^{2}+1}
\] |
[_quadrature] |
✓ |
0.492 |
|
|
\[
{}y^{\prime }+4 y = 8
\] |
[_quadrature] |
✓ |
1.681 |
|
|
\[
{}y^{\prime }+x y = 4 x
\] |
[_separable] |
✓ |
1.555 |
|
|
\[
{}y^{\prime }+4 y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.358 |
|
|
\[
{}y^{\prime } = x y-3 x -2 y+6
\] |
[_separable] |
✓ |
1.639 |
|
|
\[
{}y^{\prime } = \sin \left (x +y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.327 |
|
|
\[
{}y y^{\prime } = {\mathrm e}^{x -3 y^{2}}
\] |
[_separable] |
✓ |
1.930 |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
4.642 |
|
|
\[
{}y^{\prime } = y^{2}+9
\] |
[_quadrature] |
✓ |
6.883 |
|
|
\[
{}x y y^{\prime } = y^{2}+9
\] |
[_separable] |
✓ |
3.699 |
|
|
\[
{}y^{\prime } = \frac {1+y^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
2.345 |
|
|
\[
{}\cos \left (y\right ) y^{\prime } = \sin \left (x \right )
\] |
[_separable] |
✓ |
2.183 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 x -3 y}
\] |
[_separable] |
✓ |
2.648 |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
4.807 |
|
|
\[
{}y^{\prime } = 2 x -1+2 x y-y
\] |
[_separable] |
✓ |
2.059 |
|
|
\[
{}y y^{\prime } = x y^{2}+x
\] |
[_separable] |
✓ |
3.099 |
|
|
\[
{}y y^{\prime } = 3 \sqrt {x y^{2}+9 x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
4.914 |
|
|
\[
{}y^{\prime } = x y-4 x
\] |
[_separable] |
✓ |
1.554 |
|
|
\[
{}y^{\prime }-4 y = 2
\] |
[_quadrature] |
✓ |
1.538 |
|
|
\[
{}y y^{\prime } = x y^{2}-9 x
\] |
[_separable] |
✓ |
2.220 |
|
|
\[
{}y^{\prime } = \sin \left (y\right )
\] |
[_quadrature] |
✓ |
2.810 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x +y^{2}}
\] |
[_separable] |
✓ |
1.437 |
|
|
\[
{}y^{\prime } = 200 y-2 y^{2}
\] |
[_quadrature] |
✓ |
2.360 |
|
|
\[
{}y^{\prime } = x y-4 x
\] |
[_separable] |
✓ |
1.566 |
|
|
\[
{}y^{\prime } = x y-3 x -2 y+6
\] |
[_separable] |
✓ |
1.678 |
|
|
\[
{}y^{\prime } = 3 y^{2}-y^{2} \sin \left (x \right )
\] |
[_separable] |
✓ |
2.434 |
|
|
\[
{}y^{\prime } = \tan \left (y\right )
\] |
[_quadrature] |
✓ |
1.840 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.723 |
|
|
\[
{}y^{\prime } = \frac {6 x^{2}+4}{3 y^{2}-4 y}
\] |
[_separable] |
✓ |
1.694 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
2.398 |
|
|
\[
{}\left (y^{2}-1\right ) y^{\prime } = 4 x y^{2}
\] |
[_separable] |
✓ |
11.540 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-y}
\] |
[_quadrature] |
✓ |
1.675 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-y}+1
\] |
[_quadrature] |
✓ |
2.156 |
|
|
\[
{}y^{\prime } = 3 x y^{3}
\] |
[_separable] |
✓ |
3.746 |
|
|
\[
{}y^{\prime } = \frac {2+\sqrt {x}}{2+\sqrt {y}}
\] |
[_separable] |
✓ |
1.684 |
|
|
\[
{}y^{\prime }-3 y^{2} x^{2} = -3 x^{2}
\] |
[_separable] |
✓ |
2.088 |
|
|
\[
{}y^{\prime }-3 y^{2} x^{2} = 3 x^{2}
\] |
[_separable] |
✓ |
2.204 |
|
|
\[
{}y^{\prime } = 200 y-2 y^{2}
\] |
[_quadrature] |
✓ |
2.441 |
|
|
\[
{}y^{\prime }-2 y = -10
\] |
[_quadrature] |
✓ |
2.062 |
|
|
\[
{}y y^{\prime } = \sin \left (x \right )
\] |
[_separable] |
✓ |
3.020 |
|
|
\[
{}y^{\prime } = 2 x -1+2 x y-y
\] |
[_separable] |
✓ |
1.839 |
|
|
\[
{}x y^{\prime } = y^{2}-y
\] |
[_separable] |
✓ |
2.960 |
|