|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = 2 x +1
\] |
[_quadrature] |
✓ |
0.845 |
|
|
\[
{}y^{\prime } = \left (x -2\right )^{2}
\] |
[_quadrature] |
✓ |
0.922 |
|
|
\[
{}y^{\prime } = \sqrt {x}
\] |
[_quadrature] |
✓ |
0.431 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}}
\] |
[_quadrature] |
✓ |
0.501 |
|
|
\[
{}y^{\prime } = \frac {1}{\sqrt {x +2}}
\] |
[_quadrature] |
✓ |
0.413 |
|
|
\[
{}y^{\prime } = x \sqrt {x^{2}+9}
\] |
[_quadrature] |
✓ |
1.178 |
|
|
\[
{}y^{\prime } = \frac {10}{x^{2}+1}
\] |
[_quadrature] |
✓ |
0.626 |
|
|
\[
{}y^{\prime } = \cos \left (2 x \right )
\] |
[_quadrature] |
✓ |
0.630 |
|
|
\[
{}y^{\prime } = \frac {1}{\sqrt {-x^{2}+1}}
\] |
[_quadrature] |
✓ |
0.332 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{-x}
\] |
[_quadrature] |
✓ |
0.518 |
|
|
\[
{}x^{\prime \prime } = 50
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.050 |
|
|
\[
{}x^{\prime \prime } = -20
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.928 |
|
|
\[
{}x^{\prime \prime } = 3 t
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.044 |
|
|
\[
{}x^{\prime \prime } = 2 t +1
\] |
[[_2nd_order, _quadrature]] |
✓ |
4.813 |
|
|
\[
{}x^{\prime \prime } = 4 \left (t +3\right )^{2}
\] |
[[_2nd_order, _quadrature]] |
✓ |
4.964 |
|
|
\[
{}x^{\prime \prime } = \frac {1}{\sqrt {t +4}}
\] |
[[_2nd_order, _quadrature]] |
✓ |
4.986 |
|
|
\[
{}x^{\prime \prime } = \frac {1}{\left (t +1\right )^{3}}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.300 |
|
|
\[
{}x^{\prime \prime } = 50 \sin \left (5 t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
6.740 |
|
|
\[
{}y^{\prime } = -y-\sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.193 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.938 |
|
|
\[
{}y^{\prime } = y-\sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.088 |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.990 |
|
|
\[
{}y^{\prime } = y-x +1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.314 |
|
|
\[
{}y^{\prime } = x -y+1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.226 |
|
|
\[
{}y^{\prime } = x^{2}-y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.065 |
|
|
\[
{}y^{\prime } = x^{2}-y-2
\] |
[[_linear, ‘class A‘]] |
✓ |
1.018 |
|
|
\[
{}y^{\prime } = 2 x^{2} y^{2}
\] |
[_separable] |
✓ |
2.563 |
|
|
\[
{}y^{\prime } = x \ln \left (y\right )
\] |
[_separable] |
✓ |
1.874 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
2.033 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
1.649 |
|
|
\[
{}y^{\prime } = \sqrt {x -y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.155 |
|
|
\[
{}y^{\prime } = \sqrt {x -y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
4.244 |
|
|
\[
{}y y^{\prime } = x -1
\] |
[_separable] |
✓ |
5.393 |
|
|
\[
{}y y^{\prime } = x -1
\] |
[_separable] |
✓ |
4.251 |
|
|
\[
{}y^{\prime } = \ln \left (1+y^{2}\right )
\] |
[_quadrature] |
✓ |
1.299 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✗ |
1.628 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.189 |
|
|
\[
{}y^{\prime } = y-x
\] |
[[_linear, ‘class A‘]] |
✓ |
1.268 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}-1
\] |
[_Riccati] |
✗ |
5.830 |
|
|
\[
{}y^{\prime } = x +\frac {y^{2}}{2}
\] |
[[_Riccati, _special]] |
✓ |
1.727 |
|
|
\[
{}y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
1.390 |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
1.720 |
|
|
\[
{}y^{\prime } = y \sin \left (x \right )
\] |
[_separable] |
✓ |
1.706 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = 4 y
\] |
[_separable] |
✓ |
2.014 |
|
|
\[
{}2 \sqrt {x}\, y^{\prime } = \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
1.535 |
|
|
\[
{}y^{\prime } = 3 \sqrt {x y}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
8.986 |
|
|
\[
{}y^{\prime } = 64^{{1}/{3}} \left (x y\right )^{{1}/{3}}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
4.321 |
|
|
\[
{}y^{\prime } = 2 x \sec \left (y\right )
\] |
[_separable] |
✓ |
1.260 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 2 y
\] |
[_separable] |
✓ |
1.625 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime } = \left (1+y\right )^{2}
\] |
[_separable] |
✓ |
2.138 |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
2.479 |
|
|
\[
{}y y^{\prime } = x \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
1.900 |
|
|
\[
{}y^{3} y^{\prime } = \left (1+y^{4}\right ) \cos \left (x \right )
\] |
[_separable] |
✓ |
4.772 |
|
|
\[
{}y^{\prime } = \frac {1+\sqrt {x}}{1+\sqrt {y}}
\] |
[_separable] |
✓ |
1.427 |
|
|
\[
{}y^{\prime } = \frac {\left (x -1\right ) y^{5}}{x^{2} \left (2 y^{3}-y\right )}
\] |
[_separable] |
✓ |
1.806 |
|
|
\[
{}\left (x^{2}+1\right ) \tan \left (y\right ) y^{\prime } = x
\] |
[_separable] |
✓ |
1.674 |
|
|
\[
{}y^{\prime } = 1+x +y+x y
\] |
[_separable] |
✓ |
1.316 |
|
|
\[
{}x^{2} y^{\prime } = 1-x^{2}+y^{2}-x^{2} y^{2}
\] |
[_separable] |
✓ |
2.303 |
|
|
\[
{}y^{\prime } = y \,{\mathrm e}^{x}
\] |
[_separable] |
✓ |
1.072 |
|
|
\[
{}y^{\prime } = 3 x^{2} \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
2.718 |
|
|
\[
{}2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-16}}
\] |
[_separable] |
✓ |
2.672 |
|
|
\[
{}y^{\prime } = 4 x^{3} y-y
\] |
[_separable] |
✓ |
1.504 |
|
|
\[
{}y^{\prime }+1 = 2 y
\] |
[_quadrature] |
✓ |
1.370 |
|
|
\[
{}\tan \left (x \right ) y^{\prime } = y
\] |
[_separable] |
✓ |
2.399 |
|
|
\[
{}y^{\prime } x -y = 2 x^{2} y
\] |
[_separable] |
✓ |
1.994 |
|
|
\[
{}y^{\prime } = 2 x y^{2}+3 x^{2} y^{2}
\] |
[_separable] |
✓ |
2.089 |
|
|
\[
{}y^{\prime } = 6 \,{\mathrm e}^{2 x -y}
\] |
[_separable] |
✓ |
3.597 |
|
|
\[
{}2 \sqrt {x}\, y^{\prime } = \cos \left (y\right )^{2}
\] |
[_separable] |
✓ |
2.206 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.320 |
|
|
\[
{}{y^{\prime }}^{2} = 4 y
\] |
[_quadrature] |
✓ |
0.872 |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
1.823 |
|
|
\[
{}y^{\prime } = y \sqrt {y^{2}-1}
\] |
[_quadrature] |
✓ |
39.001 |
|
|
\[
{}y^{\prime }+y = 2
\] |
[_quadrature] |
✓ |
1.436 |
|
|
\[
{}y^{\prime }-2 y = 3 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.268 |
|
|
\[
{}y^{\prime }+3 y = 2 x \,{\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.631 |
|
|
\[
{}y^{\prime }-2 x y = {\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
1.489 |
|
|
\[
{}y^{\prime } x +2 y = 3 x
\] |
[_linear] |
✓ |
3.328 |
|
|
\[
{}y^{\prime } x +5 y = 7 x^{2}
\] |
[_linear] |
✓ |
2.097 |
|
|
\[
{}2 y^{\prime } x +y = 10 \sqrt {x}
\] |
[_linear] |
✓ |
4.525 |
|
|
\[
{}3 y^{\prime } x +y = 12 x
\] |
[_linear] |
✓ |
2.457 |
|
|
\[
{}y^{\prime } x -y = x
\] |
[_linear] |
✓ |
1.827 |
|
|
\[
{}2 y^{\prime } x -3 y = 9 x^{3}
\] |
[_linear] |
✓ |
1.565 |
|
|
\[
{}y^{\prime } x +y = 3 x y
\] |
[_separable] |
✓ |
1.764 |
|
|
\[
{}y^{\prime } x +3 y = 2 x^{5}
\] |
[_linear] |
✓ |
1.281 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.149 |
|
|
\[
{}y^{\prime } x -3 y = x^{3}
\] |
[_linear] |
✓ |
1.381 |
|
|
\[
{}y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
1.817 |
|
|
\[
{}y^{\prime } = \left (1-y\right ) \cos \left (x \right )
\] |
[_separable] |
✓ |
1.996 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+y = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.668 |
|
|
\[
{}y^{\prime } x = 2 y+x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
1.656 |
|
|
\[
{}y^{\prime }+\cot \left (x \right ) y = \cos \left (x \right )
\] |
[_linear] |
✓ |
2.124 |
|
|
\[
{}y^{\prime } = 1+x +y+x y
\] |
[_separable] |
✓ |
1.678 |
|
|
\[
{}y^{\prime } x = 3 y+x^{4} \cos \left (x \right )
\] |
[_linear] |
✓ |
2.842 |
|
|
\[
{}y^{\prime } = 2 x y+3 x^{2} {\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
2.476 |
|
|
\[
{}y^{\prime } x +\left (2 x -3\right ) y = 4 x^{4}
\] |
[_linear] |
✓ |
2.545 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime }+3 x y = x
\] |
[_separable] |
✓ |
1.835 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+3 x^{3} y = 6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}}
\] |
[_linear] |
✓ |
2.686 |
|
|
\[
{}\frac {1-4 x y^{2}}{x^{\prime }} = y^{3}
\] |
[_linear] |
✓ |
1.492 |
|
|
\[
{}\frac {x+y \,{\mathrm e}^{y}}{x^{\prime }} = 1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.324 |
|
|
\[
{}\frac {1+2 x y}{x^{\prime }} = y^{2}+1
\] |
[_linear] |
✓ |
1.461 |
|