|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = 2 x +1
\] |
[_quadrature] |
✓ |
0.426 |
|
|
\[
{}y^{\prime } = \left (-2+x \right )^{2}
\] |
[_quadrature] |
✓ |
0.487 |
|
|
\[
{}y^{\prime } = \sqrt {x}
\] |
[_quadrature] |
✓ |
0.510 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}}
\] |
[_quadrature] |
✓ |
0.476 |
|
|
\[
{}y^{\prime } = \frac {1}{\sqrt {x +2}}
\] |
[_quadrature] |
✓ |
0.549 |
|
|
\[
{}y^{\prime } = x \sqrt {x^{2}+9}
\] |
[_quadrature] |
✓ |
0.875 |
|
|
\[
{}y^{\prime } = \frac {10}{x^{2}+1}
\] |
[_quadrature] |
✓ |
0.559 |
|
|
\[
{}y^{\prime } = \cos \left (2 x \right )
\] |
[_quadrature] |
✓ |
0.636 |
|
|
\[
{}y^{\prime } = \frac {1}{\sqrt {-x^{2}+1}}
\] |
[_quadrature] |
✓ |
0.676 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{-x}
\] |
[_quadrature] |
✓ |
0.533 |
|
|
\[
{}x^{\prime \prime } = 50
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.015 |
|
|
\[
{}x^{\prime \prime } = -20
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.017 |
|
|
\[
{}x^{\prime \prime } = 3 t
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.540 |
|
|
\[
{}x^{\prime \prime } = 2 t +1
\] |
[[_2nd_order, _quadrature]] |
✓ |
4.871 |
|
|
\[
{}x^{\prime \prime } = 4 \left (3+t \right )^{2}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.698 |
|
|
\[
{}x^{\prime \prime } = \frac {1}{\sqrt {t +4}}
\] |
[[_2nd_order, _quadrature]] |
✓ |
5.714 |
|
|
\[
{}x^{\prime \prime } = \frac {1}{\left (t +1\right )^{3}}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.867 |
|
|
\[
{}x^{\prime \prime } = 50 \sin \left (5 t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
6.967 |
|
|
\[
{}y^{\prime } = -y-\sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.254 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.053 |
|
|
\[
{}y^{\prime } = y-\sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.272 |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.016 |
|
|
\[
{}y^{\prime } = y-x +1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.176 |
|
|
\[
{}y^{\prime } = x +1-y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.187 |
|
|
\[
{}y^{\prime } = x^{2}-y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.047 |
|
|
\[
{}y^{\prime } = x^{2}-y-2
\] |
[[_linear, ‘class A‘]] |
✓ |
1.075 |
|
|
\[
{}y^{\prime } = 2 x^{2} y^{2}
\] |
[_separable] |
✓ |
2.201 |
|
|
\[
{}y^{\prime } = x \ln \left (y\right )
\] |
[_separable] |
✓ |
2.082 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
2.098 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
1.823 |
|
|
\[
{}y^{\prime } = \sqrt {x -y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.538 |
|
|
\[
{}y^{\prime } = \sqrt {x -y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
4.248 |
|
|
\[
{}y y^{\prime } = x -1
\] |
[_separable] |
✓ |
5.044 |
|
|
\[
{}y y^{\prime } = x -1
\] |
[_separable] |
✓ |
3.921 |
|
|
\[
{}y^{\prime } = \ln \left (1+y^{2}\right )
\] |
[_quadrature] |
✓ |
1.316 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✗ |
1.612 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.291 |
|
|
\[
{}y^{\prime } = y-x
\] |
[[_linear, ‘class A‘]] |
✓ |
1.362 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}-1
\] |
[_Riccati] |
✗ |
4.654 |
|
|
\[
{}y^{\prime } = x +\frac {y^{2}}{2}
\] |
[[_Riccati, _special]] |
✓ |
1.718 |
|
|
\[
{}y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
1.261 |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
1.587 |
|
|
\[
{}y^{\prime } = y \sin \left (x \right )
\] |
[_separable] |
✓ |
1.451 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = 4 y
\] |
[_separable] |
✓ |
1.704 |
|
|
\[
{}2 \sqrt {x}\, y^{\prime } = \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
1.591 |
|
|
\[
{}y^{\prime } = 3 \sqrt {x y}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
8.607 |
|
|
\[
{}y^{\prime } = 64^{{1}/{3}} \left (x y\right )^{{1}/{3}}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.882 |
|
|
\[
{}y^{\prime } = 2 x \sec \left (y\right )
\] |
[_separable] |
✓ |
1.204 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 2 y
\] |
[_separable] |
✓ |
1.467 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime } = \left (y+1\right )^{2}
\] |
[_separable] |
✓ |
1.918 |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
2.224 |
|
|
\[
{}y y^{\prime } = x \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
1.791 |
|
|
\[
{}y^{3} y^{\prime } = \left (1+y^{4}\right ) \cos \left (x \right )
\] |
[_separable] |
✓ |
5.016 |
|
|
\[
{}y^{\prime } = \frac {1+\sqrt {x}}{1+\sqrt {y}}
\] |
[_separable] |
✓ |
1.593 |
|
|
\[
{}y^{\prime } = \frac {\left (x -1\right ) y^{5}}{x^{2} \left (2 y^{3}-y\right )}
\] |
[_separable] |
✓ |
1.776 |
|
|
\[
{}\left (x^{2}+1\right ) \tan \left (y\right ) y^{\prime } = x
\] |
[_separable] |
✓ |
1.730 |
|
|
\[
{}y^{\prime } = 1+x +y+x y
\] |
[_separable] |
✓ |
1.234 |
|
|
\[
{}x^{2} y^{\prime } = 1-x^{2}+y^{2}-x^{2} y^{2}
\] |
[_separable] |
✓ |
2.239 |
|
|
\[
{}y^{\prime } = y \,{\mathrm e}^{x}
\] |
[_separable] |
✓ |
1.471 |
|
|
\[
{}y^{\prime } = 3 x^{2} \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
4.203 |
|
|
\[
{}2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-16}}
\] |
[_separable] |
✓ |
2.943 |
|
|
\[
{}y^{\prime } = 4 x^{3} y-y
\] |
[_separable] |
✓ |
1.675 |
|
|
\[
{}1+y^{\prime } = 2 y
\] |
[_quadrature] |
✓ |
1.339 |
|
|
\[
{}\tan \left (x \right ) y^{\prime } = y
\] |
[_separable] |
✓ |
2.179 |
|
|
\[
{}x y^{\prime }-y = 2 x^{2} y
\] |
[_separable] |
✓ |
1.877 |
|
|
\[
{}y^{\prime } = 2 x y^{2}+3 x^{2} y^{2}
\] |
[_separable] |
✓ |
2.013 |
|
|
\[
{}y^{\prime } = 6 \,{\mathrm e}^{2 x -y}
\] |
[_separable] |
✓ |
3.246 |
|
|
\[
{}2 \sqrt {x}\, y^{\prime } = \cos \left (y\right )^{2}
\] |
[_separable] |
✓ |
2.339 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.116 |
|
|
\[
{}{y^{\prime }}^{2} = 4 y
\] |
[_quadrature] |
✓ |
0.693 |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
1.559 |
|
|
\[
{}y^{\prime } = y \sqrt {y^{2}-1}
\] |
[_quadrature] |
✓ |
23.726 |
|
|
\[
{}y^{\prime }+y = 2
\] |
[_quadrature] |
✓ |
1.275 |
|
|
\[
{}y^{\prime }-2 y = 3 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.334 |
|
|
\[
{}y^{\prime }+3 y = 2 x \,{\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.583 |
|
|
\[
{}y^{\prime }-2 x y = {\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
1.442 |
|
|
\[
{}x y^{\prime }+2 y = 3 x
\] |
[_linear] |
✓ |
2.763 |
|
|
\[
{}x y^{\prime }+5 y = 7 x^{2}
\] |
[_linear] |
✓ |
1.868 |
|
|
\[
{}2 x y^{\prime }+y = 10 \sqrt {x}
\] |
[_linear] |
✓ |
4.156 |
|
|
\[
{}3 x y^{\prime }+y = 12 x
\] |
[_linear] |
✓ |
2.058 |
|
|
\[
{}x y^{\prime }-y = x
\] |
[_linear] |
✓ |
1.640 |
|
|
\[
{}2 x y^{\prime }-3 y = 9 x^{3}
\] |
[_linear] |
✓ |
1.431 |
|
|
\[
{}x y^{\prime }+y = 3 x y
\] |
[_separable] |
✓ |
1.665 |
|
|
\[
{}x y^{\prime }+3 y = 2 x^{5}
\] |
[_linear] |
✓ |
1.734 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.344 |
|
|
\[
{}x y^{\prime }-3 y = x^{3}
\] |
[_linear] |
✓ |
1.414 |
|
|
\[
{}y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
1.538 |
|
|
\[
{}y^{\prime } = \left (1-y\right ) \cos \left (x \right )
\] |
[_separable] |
✓ |
1.887 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+y = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.728 |
|
|
\[
{}x y^{\prime } = 2 y+x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
1.700 |
|
|
\[
{}y^{\prime }+\cot \left (x \right ) y = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.755 |
|
|
\[
{}y^{\prime } = 1+x +y+x y
\] |
[_separable] |
✓ |
1.562 |
|
|
\[
{}x y^{\prime } = 3 y+x^{4} \cos \left (x \right )
\] |
[_linear] |
✓ |
2.675 |
|
|
\[
{}y^{\prime } = 2 x y+3 x^{2} {\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
2.698 |
|
|
\[
{}x y^{\prime }+\left (2 x -3\right ) y = 4 x^{4}
\] |
[_linear] |
✓ |
2.376 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime }+3 x y = x
\] |
[_separable] |
✓ |
2.028 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+3 x^{3} y = 6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}}
\] |
[_linear] |
✓ |
2.321 |
|
|
\[
{}\frac {1-4 x y^{2}}{x^{\prime }} = y^{3}
\] |
[_linear] |
✓ |
1.348 |
|
|
\[
{}\frac {x+y \,{\mathrm e}^{y}}{x^{\prime }} = 1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.381 |
|
|
\[
{}\frac {1+2 x y}{x^{\prime }} = y^{2}+1
\] |
[_linear] |
✓ |
1.360 |
|